Dataset Viewer
id
string | setting_key
string | difficulty
string | level
int32 | messages
dict | ground_truth
string | dataset
string | omega_split
string |
|---|---|---|---|---|---|---|---|
math_algebra_func_area_level_4_4_0
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -3|(-2(-3sin(1π(-3|(-4x^2 + 5x + 3) - 1|) - 3) - 2)^2 + 3(-3sin(1π(-3|(-4x^2 + 5x + 3) - 1|) - 3) - 2) + 4) - 1| - 2, g(x) = -1(-1(1(-5x - 3))^2 - 3(1(-5x - 3)) - 2) - 4, x = -0.3, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
7.0
|
math
|
train
|
math_algebra_func_area_level_4_4_1
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 4(3|(5(3|(-3|x - 3| - 3) + 3| - 2) - 3) - 2|)^2 - 4(3|(5(3|(-3|x - 3| - 3) + 3| - 2) - 3) - 2|) + 1 and g(x) = (-1(3(-4((1x + 3)/(-3x + 2)) + 5)^2 - 1(-4((1x + 3)/(-3x + 2)) + 5) + 5) - 3)/(-1(3(-4((1x + 3)/(-3x + 2)) + 5)^2 - 1(-4((1x + 3)/(-3x + 2)) + 5) + 5)) from x = 2.7 to x = 2.8000000000000003. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
52.2
|
math
|
train
|
math_algebra_func_area_level_4_4_2
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3((3(-2(3e^(2(5x - 1)) + 1)^2 - 3(3e^(2(5x - 1)) + 1)) - 2)/(1(-2(3e^(2(5x - 1)) + 1)^2 - 3(3e^(2(5x - 1)) + 1)) + 3))^2 - 5((3(-2(3e^(2(5x - 1)) + 1)^2 - 3(3e^(2(5x - 1)) + 1)) - 2)/(1(-2(3e^(2(5x - 1)) + 1)^2 - 3(3e^(2(5x - 1)) + 1)) + 3)) + 4, g(x) = (3(-4(-3|(1x - 2) + 2| + 1)^2 - 4(-3|(1x - 2) + 2| + 1) + 2) - 3)/(3(-4(-3|(1x - 2) + 2| + 1)^2 - 4(-3|(1x - 2) + 2| + 1) + 2) + 1), x = 0.2, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9.8
|
math
|
train
|
math_algebra_func_area_level_4_4_3
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-1(-2sin(2π(1(2(-3x^2 + 1x + 2) - 2) - 5) - 3)) + 3)/(3(-2sin(2π(1(2(-3x^2 + 1x + 2) - 2) - 5) - 3))) and g(x) = -1(3((-2(-2|x + 2| - 1) - 3)/(1(-2|x + 2| - 1) + 2)) - 5)^2 - 5(3((-2(-2|x + 2| - 1) - 3)/(1(-2|x + 2| - 1) + 2)) - 5) + 4 between the vertical lines x = -1.8 and x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.6
|
math
|
train
|
math_algebra_func_area_level_4_4_4
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-3(1sin(1π(1(5(4x - 4) - 2) - 4) + 1) + 1) + 1)/(-3(1sin(1π(1(5(4x - 4) - 2) - 4) + 1) + 1)), g(x) = -4(-1(-3(-2|x + 1|)^2 + 5(-2|x + 1|) + 5)^2 + 2(-3(-2|x + 1|)^2 + 5(-2|x + 1|) + 5))^2 - 5(-1(-3(-2|x + 1|)^2 + 5(-2|x + 1|) + 5)^2 + 2(-3(-2|x + 1|)^2 + 5(-2|x + 1|) + 5)) + 2, x = -1.2, and x = -1.0999999999999999. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
11.3
|
math
|
train
|
math_algebra_func_area_level_4_4_5
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -4(4(-3cos(1π(3|(1x + 5) - 1| - 1) - 1) - 2)^2 - 1(-3cos(1π(3|(1x + 5) - 1| - 1) - 1) - 2) - 5) + 4 and g(x) = (-3(-3|(-2(-2|x| + 1) - 1) - 2|) + 1)/(3(-3|(-2(-2|x| + 1) - 1) - 2|) + 1) from x = -1.2 to x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.2
|
math
|
train
|
math_algebra_func_area_level_4_4_6
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (1(1(-1(-1(5x - 4) + 3)^2 + 5(-1(5x - 4) + 3) + 1) - 1) - 2)/(-2(1(-1(-1(5x - 4) + 3)^2 + 5(-1(5x - 4) + 3) + 1) - 1)) and g(x) = -1|(4(-2(-2|x + 1| - 1)^2 + 1(-2|x + 1| - 1) + 4) + 5)| between the vertical lines x = -1.2 and x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.6
|
math
|
train
|
math_algebra_func_area_level_4_4_7
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3|(2|(-4(2e^(2(-1x + 3)) - 1) - 2) + 1| - 2) + 2| - 2, g(x) = -2|(2|(1sin(1π(2x^2 + 1x + 5) + 2) + 2)| - 2) - 2| + 2, x = 3.4, and x = 3.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_8
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1(-1|(-3|(-3(-2x + 1) - 2)|) - 1|)^2 - 5(-1|(-3|(-3(-2x + 1) - 2)|) - 1|) - 2, g(x) = 3((-1(2(4x + 1)^2 - 5(4x + 1)) + 3)/(2(2(4x + 1)^2 - 5(4x + 1)) + 1))^2 + 4((-1(2(4x + 1)^2 - 5(4x + 1)) + 3)/(2(2(4x + 1)^2 - 5(4x + 1)) + 1)) - 2, x = -0.2, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
154.2
|
math
|
train
|
math_algebra_func_area_level_4_4_9
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1(-2(-5(3|(-1x^2 + 5x - 4) - 2| - 3) - 2) - 5) - 2)/(-2(-2(-5(3|(-1x^2 + 5x - 4) - 2| - 3) - 2) - 5) - 2) and g(x) = -1(3|(4((1x + 3)/(-1x - 2))^2 + 4((1x + 3)/(-1x - 2)) - 4) - 3| - 2)^2 - 4(3|(4((1x + 3)/(-1x - 2))^2 + 4((1x + 3)/(-1x - 2)) - 4) - 3| - 2) + 4 from x = -2.6 to x = -2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.5
|
math
|
train
|
math_algebra_func_area_level_4_4_10
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (2(1((-3(2sin(2π(2x + 5)) + 3) - 3)/(-1(2sin(2π(2x + 5)) + 3) - 2))^2 - 2((-3(2sin(2π(2x + 5)) + 3) - 3)/(-1(2sin(2π(2x + 5)) + 3) - 2)) - 1) + 1)/(-1(1((-3(2sin(2π(2x + 5)) + 3) - 3)/(-1(2sin(2π(2x + 5)) + 3) - 2))^2 - 2((-3(2sin(2π(2x + 5)) + 3) - 3)/(-1(2sin(2π(2x + 5)) + 3) - 2)) - 1)), g(x) = 3(-2((-1((-1x + 2)/(1x)) - 2)/(-3((-1x + 2)/(1x)) + 2))^2 - 4) - 3, x = -2.0, and x = -1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
7.0
|
math
|
train
|
math_algebra_func_area_level_4_4_11
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1(-1|(2|(-2|(-1x^2 - 2x) + 1| - 3) - 1| - 2) + 3| - 3) - 1)/(2(-1|(2|(-2|(-1x^2 - 2x) + 1| - 3) - 1| - 2) + 3| - 3) - 1) and g(x) = 2(-3|(2(2x + 2)^2 - 3) + 1| + 3) - 4 from x = -1.5 to x = -1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_12
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2((2(-1|(2sin(2π(-3x^2 - 5x + 1) - 3) - 2) - 2| - 1) + 3)/(-2(-1|(2sin(2π(-3x^2 - 5x + 1) - 3) - 2) - 2| - 1) + 3)) - 1 and g(x) = 1cos(3π(-5(-3((2x - 2)/(-1x + 3)) - 4)^2 - 3(-3((2x - 2)/(-1x + 3)) - 4) - 1) + 3) + 1 from x = 4.7 to x = 4.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_13
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1|(-1|(4(-1|(3sin(1πx - 1) + 2) - 3| + 1) + 5)| + 1) + 1| + 1 and g(x) = 2(-5((-1(2|x + 2| + 1) + 3)/(3(2|x + 2| + 1)))) + 1 between the vertical lines x = 1.6 and x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.8
|
math
|
train
|
math_algebra_func_area_level_4_4_14
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (2(2|(5(-1((-2x + 2)/(-2x + 1))^2 + 5((-2x + 2)/(-2x + 1)) + 5) - 3) + 3| + 2) - 3)/(-1(2|(5(-1((-2x + 2)/(-2x + 1))^2 + 5((-2x + 2)/(-2x + 1)) + 5) - 3) + 3| + 2) + 3), g(x) = (1((-2(-1(-3x - 4)^2 + 1) - 2)/(-2(-1(-3x - 4)^2 + 1) + 3)) - 1)/(1((-2(-1(-3x - 4)^2 + 1) - 2)/(-2(-1(-3x - 4)^2 + 1) + 3)) + 1), x = -1.7, and x = -0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
12.4
|
math
|
train
|
math_algebra_func_area_level_4_4_15
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -3(-3|(2(-2e^(1(-5x^2 + 2x + 1)) + 2) - 4) + 1| + 1) - 4, g(x) = -2(5(-3|(2cos(1πx + 3) + 2) - 3| + 2) + 3) + 1, x = 2.6, and x = 2.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.5
|
math
|
train
|
math_algebra_func_area_level_4_4_16
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1(3((3(2(-3x + 5) - 2) - 3)/(-1(2(-3x + 5) - 2) + 3))^2 - 4) + 4, g(x) = 3cos(1π((-1((-1(-5x - 3) + 2)/(3(-5x - 3) - 1)) - 1)/(-3((-1(-5x - 3) + 2)/(3(-5x - 3) - 1)) - 2)) + 1) + 2, x = 1.0, and x = 1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.2
|
math
|
train
|
math_algebra_func_area_level_4_4_17
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -4((3((-1(-3|(1x + 4) + 3| - 2) - 2)/(3(-3|(1x + 4) + 3| - 2) - 2)) - 1)/(-1((-1(-3|(1x + 4) + 3| - 2) - 2)/(3(-3|(1x + 4) + 3| - 2) - 2)) - 1))^2 - 5((3((-1(-3|(1x + 4) + 3| - 2) - 2)/(3(-3|(1x + 4) + 3| - 2) - 2)) - 1)/(-1((-1(-3|(1x + 4) + 3| - 2) - 2)/(3(-3|(1x + 4) + 3| - 2) - 2)) - 1)) + 2, g(x) = -2|(3|((1(1|x - 2| - 2) + 1)/(3(1|x - 2| - 2) + 2)) + 1| - 3)| - 3, x = 0.7, and x = 3.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
97.4
|
math
|
train
|
math_algebra_func_area_level_4_4_18
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2(-1((-2((-1(2|x - 2|) - 3)/(-2(2|x - 2|) - 1)) + 3)/(1((-1(2|x - 2|) - 3)/(-2(2|x - 2|) - 1))))^2 + 1((-2((-1(2|x - 2|) - 3)/(-2(2|x - 2|) - 1)) + 3)/(1((-1(2|x - 2|) - 3)/(-2(2|x - 2|) - 1)))) - 4)^2 + 1(-1((-2((-1(2|x - 2|) - 3)/(-2(2|x - 2|) - 1)) + 3)/(1((-1(2|x - 2|) - 3)/(-2(2|x - 2|) - 1))))^2 + 1((-2((-1(2|x - 2|) - 3)/(-2(2|x - 2|) - 1)) + 3)/(1((-1(2|x - 2|) - 3)/(-2(2|x - 2|) - 1)))) - 4) + 4 and g(x) = (1((1((-1(2|x + 1| - 2) + 3)/(-2(2|x + 1| - 2) - 3)) + 2)/(-3((-1(2|x + 1| - 2) + 3)/(-2(2|x + 1| - 2) - 3)) + 1)) - 2)/(3((1((-1(2|x + 1| - 2) + 3)/(-2(2|x + 1| - 2) - 3)) + 2)/(-3((-1(2|x + 1| - 2) + 3)/(-2(2|x + 1| - 2) - 3)) + 1)) - 1) between the vertical lines x = -2.1 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
246.6
|
math
|
train
|
math_algebra_func_area_level_4_4_19
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -5(-2e^(1(3|(2(-3x - 1)^2 + 3(-3x - 1) - 3)| - 3)) - 1) + 1 and g(x) = 3|(3cos(3π((-2(-4x) - 3)/(-1(-4x) - 3)) + 2) - 1) + 2| - 2 from x = 0.4 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.5
|
math
|
train
|
math_algebra_func_area_level_4_4_20
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 5(2(1|(1|(-3|x - 1| + 1) - 3| + 1) + 3|) - 5) + 1 and g(x) = (2(-3|(-2((-1x + 3)/(-3x - 1))^2 + 5((-1x + 3)/(-3x - 1)) + 5) - 3| + 1) + 3)/(-1(-3|(-2((-1x + 3)/(-3x - 1))^2 + 5((-1x + 3)/(-3x - 1)) + 5) - 3| + 1) - 2) from x = 1.0 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
40.0
|
math
|
train
|
math_algebra_func_area_level_4_4_21
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(-1|(-2|((-3(1x^2 - 4x + 1))/(1(1x^2 - 4x + 1) + 3)) - 1| - 1) + 3| - 3) + 2)/(-1(-1|(-2|((-3(1x^2 - 4x + 1))/(1(1x^2 - 4x + 1) + 3)) - 1| - 1) + 3| - 3) - 1) and g(x) = 5(3|((1(1x^2 - 5x))/(-1(1x^2 - 5x) + 2)) + 3| - 3) + 5 from x = -0.6 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.7
|
math
|
train
|
math_algebra_func_area_level_4_4_22
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2|(2(-2sin(3π(5(-3|x + 2| + 3)^2) - 2) + 2)^2) - 1| - 2 and g(x) = -1|(-3|((2(-2|x + 3| - 3) - 2)/(2(-2|x + 3| - 3) + 1)) + 1| + 3) - 2| between the vertical lines x = -2.3 and x = -2.1999999999999997. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.1
|
math
|
train
|
math_algebra_func_area_level_4_4_23
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -4((-3(1(2(-3|x + 1|) + 3)^2 + 1(2(-3|x + 1|) + 3) + 4) - 2)/(-1(1(2(-3|x + 1|) + 3)^2 + 1(2(-3|x + 1|) + 3) + 4) + 2))^2 + 2((-3(1(2(-3|x + 1|) + 3)^2 + 1(2(-3|x + 1|) + 3) + 4) - 2)/(-1(1(2(-3|x + 1|) + 3)^2 + 1(2(-3|x + 1|) + 3) + 4) + 2)) + 2 and g(x) = -3((1(3(-3x + 1)^2 - 5(-3x + 1) - 4) - 2)/(-1(3(-3x + 1)^2 - 5(-3x + 1) - 4) - 2)) from x = -0.3 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
77.1
|
math
|
train
|
math_algebra_func_area_level_4_4_24
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2(2((3(-2(-1x^2 + 3x - 1) - 1) - 1)/(2(-2(-1x^2 + 3x - 1) - 1) - 1)))^2 + 3, g(x) = 2|(-4((-2(1|x - 3| + 3) - 1)/(-3(1|x - 3| + 3) - 1))^2 + 2) + 1| + 2, x = 0.1, and x = 2.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
38.2
|
math
|
train
|
math_algebra_func_area_level_4_4_25
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -3|(2|(2e^(2(-2|(1|x - 2| + 1) + 2| - 3)) - 2) + 2| - 3)| - 1, g(x) = -1|(-1|(1(-3|x - 1| - 2)^2 + 5(-3|x - 1| - 2) + 2) - 3| - 1) + 1| + 2, x = -0.6, and x = 2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
21.8
|
math
|
train
|
math_algebra_func_area_level_4_4_26
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 4((-1(1(2e^(2((-2x - 2)/(-1x))) - 1) + 3) + 3)/(-2(1(2e^(2((-2x - 2)/(-1x))) - 1) + 3) + 3)) - 4, g(x) = -3(3(-2((-3x + 3)/(1x + 1)) + 4) - 3)^2 + 3, x = 0.3, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_4_4_27
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 4(1|(-2|(4((-3x + 3)/(2x))^2 - 5((-3x + 3)/(2x)) - 2) + 3| - 3) + 3|)^2 + 5(1|(-2|(4((-3x + 3)/(2x))^2 - 5((-3x + 3)/(2x)) - 2) + 3| - 3) + 3|) - 5 and g(x) = -2e^(2(-3((3(-2|x - 1| - 2) + 3)/(3(-2|x - 1| - 2) - 2))^2 + 3((3(-2|x - 1| - 2) + 3)/(3(-2|x - 1| - 2) - 2)) - 1)) - 1 between the vertical lines x = 0.8 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_28
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -3|(3(5((1(1|x + 1| - 3) + 1)/(2(1|x + 1| - 3) - 1))^2 + 5((1(1|x + 1| - 3) + 1)/(2(1|x + 1| - 3) - 1)) + 1) + 2) + 1| + 2, g(x) = (3(3|(3((-1x - 1)/(-1x + 3))^2 + 2((-1x - 1)/(-1x + 3)) - 2) + 2| - 1) + 2)/(-2(3|(3((-1x - 1)/(-1x + 3))^2 + 2((-1x - 1)/(-1x + 3)) - 2) + 2| - 1) + 3), x = -2.8, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
121.9
|
math
|
train
|
math_algebra_func_area_level_4_4_29
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2((-3(5(3cos(1π((2x - 2)/(-1x + 2)) + 2) + 3) - 5))/(2(5(3cos(1π((2x - 2)/(-1x + 2)) + 2) + 3) - 5) + 1)) - 5 and g(x) = -2|(-3e^(2((3(1x + 5) - 1)/(1(1x + 5) + 3))) - 3) + 2| + 3 from x = -4.4 to x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
158.6
|
math
|
train
|
math_algebra_func_area_level_4_4_30
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 4(-3|(-1(-1|(-1cos(3πx + 2) + 2) + 1|)^2 + 1(-1|(-1cos(3πx + 2) + 2) + 1|)) - 1| - 2) + 3 and g(x) = -2e^(-1(1((2((2x - 2)/(1x + 3)) - 3)/(3((2x - 2)/(1x + 3)) + 3))^2 + 5((2((2x - 2)/(1x + 3)) - 3)/(3((2x - 2)/(1x + 3)) + 3)) + 2)) - 1 between the vertical lines x = 0.4 and x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.8
|
math
|
train
|
math_algebra_func_area_level_4_4_31
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2(3|(3|(-4((1x + 1)/(-3x + 1))^2 - 1((1x + 1)/(-3x + 1)) + 3) + 1| + 1) - 3| - 3)^2 + 3(3|(3|(-4((1x + 1)/(-3x + 1))^2 - 1((1x + 1)/(-3x + 1)) + 3) + 1| + 1) - 3| - 3) - 2 and g(x) = 3|(-4(-1(-1x^2 - 5x + 2))^2 + 2(-1(-1x^2 - 5x + 2)) - 4) - 3| - 2 between the vertical lines x = -0.1 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
8.9
|
math
|
train
|
math_algebra_func_area_level_4_4_32
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1|((-2((2(2(4x^2 + 5x - 3)) - 2)/(2(2(4x^2 + 5x - 3)) + 2)))/(1((2(2(4x^2 + 5x - 3)) - 2)/(2(2(4x^2 + 5x - 3)) + 2)) + 2)) + 3| - 3 and g(x) = (2(1|(5(-1sin(1πx - 2) - 1)^2 - 4(-1sin(1πx - 2) - 1) - 2) - 1| + 1) + 1)/(-1(1|(5(-1sin(1πx - 2) - 1)^2 - 4(-1sin(1πx - 2) - 1) - 2) - 1| + 1) + 3) between the vertical lines x = -4.3 and x = -3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
34.9
|
math
|
train
|
math_algebra_func_area_level_4_4_33
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -4(5((2((-3(-1x + 5) + 3)/(3(-1x + 5) - 2)) - 3)/(-2((-3(-1x + 5) + 3)/(3(-1x + 5) - 2)))) + 4) + 3, g(x) = (-3(3cos(2π((-1((3x + 3)/(1x)) + 1)/(2((3x + 3)/(1x)) - 1)) + 3) - 3) + 1)/(-3(3cos(2π((-1((3x + 3)/(1x)) + 1)/(2((3x + 3)/(1x)) - 1)) + 3) - 3) - 3), x = -1.2, and x = -1.0999999999999999. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.8
|
math
|
train
|
math_algebra_func_area_level_4_4_34
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2|((-3(3(2cos(3π((-1x + 3)/(-3x + 1)) - 3) - 2) - 5) + 3)/(3(3(2cos(3π((-1x + 3)/(-3x + 1)) - 3) - 2) - 5) - 2)) + 3| and g(x) = -1(-1(5((3x - 3)/(1x + 3))^2 + 1((3x - 3)/(1x + 3)) - 2)^2 + 1(5((3x - 3)/(1x + 3))^2 + 1((3x - 3)/(1x + 3)) - 2)) - 4 from x = 1.8 to x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_35
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2e^(1(-5(-4(-1(1x^2 - 4x + 2)^2 - 1(1x^2 - 4x + 2))^2 + 3(-1(1x^2 - 4x + 2)^2 - 1(1x^2 - 4x + 2)) + 2))) + 2, g(x) = (-2(1(-2(3cos(1πx + 2) + 1)^2 - 3(3cos(1πx + 2) + 1) - 5) - 5) + 1)/(-1(1(-2(3cos(1πx + 2) + 1)^2 - 3(3cos(1πx + 2) + 1) - 5) - 5) + 2), x = 2.8, and x = 3.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_4_4_36
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 3((-2((-3((3(2|x + 2| + 3) + 3)/(-1(2|x + 2| + 3) - 3)) - 2)/(1((3(2|x + 2| + 3) + 3)/(-1(2|x + 2| + 3) - 3)) + 2)) + 3)/(-3((-3((3(2|x + 2| + 3) + 3)/(-1(2|x + 2| + 3) - 3)) - 2)/(1((3(2|x + 2| + 3) + 3)/(-1(2|x + 2| + 3) - 3)) + 2)) + 4)) and g(x) = (2(3|(-2cos(1π(1x) + 2)) - 2|) - 1)/(-2(3|(-2cos(1π(1x) + 2)) - 2|) + 3) between the vertical lines x = 4.2 and x = 4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.6
|
math
|
train
|
math_algebra_func_area_level_4_4_37
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (1((2(-1(-3(-1|x - 1|)^2 - 5(-1|x - 1|) - 4)^2 - 2(-3(-1|x - 1|)^2 - 5(-1|x - 1|) - 4) + 1) + 1)/(2(-1(-3(-1|x - 1|)^2 - 5(-1|x - 1|) - 4)^2 - 2(-3(-1|x - 1|)^2 - 5(-1|x - 1|) - 4) + 1) + 2)) - 1)/(2((2(-1(-3(-1|x - 1|)^2 - 5(-1|x - 1|) - 4)^2 - 2(-3(-1|x - 1|)^2 - 5(-1|x - 1|) - 4) + 1) + 1)/(2(-1(-3(-1|x - 1|)^2 - 5(-1|x - 1|) - 4)^2 - 2(-3(-1|x - 1|)^2 - 5(-1|x - 1|) - 4) + 1) + 2)) - 1), g(x) = 5((-3(-1|(2|x + 2| - 3) + 3|) - 1)/(3(-1|(2|x + 2| - 3) + 3|) + 2))^2 + 4((-3(-1|(2|x + 2| - 3) + 3|) - 1)/(3(-1|(2|x + 2| - 3) + 3|) + 2)) + 2, x = -0.3, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
7.0
|
math
|
train
|
math_algebra_func_area_level_4_4_38
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1(3(2sin(2π(1(-4x - 1)^2 + 2(-4x - 1) + 2) - 3) + 2)^2 + 1(2sin(2π(1(-4x - 1)^2 + 2(-4x - 1) + 2) - 3) + 2) - 3))/(-1(3(2sin(2π(1(-4x - 1)^2 + 2(-4x - 1) + 2) - 3) + 2)^2 + 1(2sin(2π(1(-4x - 1)^2 + 2(-4x - 1) + 2) - 3) + 2) - 3) - 2), g(x) = -3(4(-2|(2x - 1) - 3| - 1) - 5) + 5, x = 0.6, and x = 0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9.5
|
math
|
train
|
math_algebra_func_area_level_4_4_39
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2(1(1(-2((2x - 3)/(-2x - 1)) - 1))^2 + 4(1(-2((2x - 3)/(-2x - 1)) - 1)) - 1) - 4 and g(x) = -3((1((1(2x - 2) - 3)/(3(2x - 2) + 2)))/(-3((1(2x - 2) - 3)/(3(2x - 2) + 2)) + 4)) - 3 from x = 0.1 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_40
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 5(1|(1((1((1x + 1)/(2x + 2)) - 3)/(-1((1x + 1)/(2x + 2))))^2 - 3((1((1x + 1)/(2x + 2)) - 3)/(-1((1x + 1)/(2x + 2)))) + 3) + 3| - 3)^2 - 3(1|(1((1((1x + 1)/(2x + 2)) - 3)/(-1((1x + 1)/(2x + 2))))^2 - 3((1((1x + 1)/(2x + 2)) - 3)/(-1((1x + 1)/(2x + 2)))) + 3) + 3| - 3) + 3, g(x) = 5(3((-2(2x) - 1)/(-1(2x) - 3))^2 - 2((-2(2x) - 1)/(-1(2x) - 3)) + 3) + 1, x = -2.0, and x = -1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
-27362.3
|
math
|
train
|
math_algebra_func_area_level_4_4_41
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 3(4(-3cos(1π((2((1x - 3)/(-2x - 3)) - 3)/(1((1x - 3)/(-2x - 3)) + 1)) + 3) + 1)^2 + 5(-3cos(1π((2((1x - 3)/(-2x - 3)) - 3)/(1((1x - 3)/(-2x - 3)) + 1)) + 3) + 1) - 1) + 3 and g(x) = 1|((-1(-2|(3e^(-2x) + 3) - 3|) + 1)/(3(-2|(3e^(-2x) + 3) - 3|) + 1))| + 2 between the vertical lines x = -3.7 and x = -3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.8
|
math
|
train
|
math_algebra_func_area_level_4_4_42
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2|(-3(-2(2|(3|x - 1| + 1) - 1| - 2)^2 - 1(2|(3|x - 1| + 1) - 1| - 2) + 2)^2 + 5(-2(2|(3|x - 1| + 1) - 1| - 2)^2 - 1(2|(3|x - 1| + 1) - 1| - 2) + 2) - 4) + 2| + 2 and g(x) = -2cos(2π((-3((-2(3x^2 - 1x - 3) + 1)/(3(3x^2 - 1x - 3) - 1)) - 1)/(-1((-2(3x^2 - 1x - 3) + 1)/(3(3x^2 - 1x - 3) - 1)) - 3)) + 1) - 3 between the vertical lines x = 1.4 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_4_4_43
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2((1((3(-2|(3x - 2) - 1| - 3) + 1)/(-2(-2|(3x - 2) - 1| - 3))) + 1)/(-2((3(-2|(3x - 2) - 1| - 3) + 1)/(-2(-2|(3x - 2) - 1| - 3))) - 1)) - 2 and g(x) = -2|((-1((-2(-2x^2 + 4x + 3) - 3)/(2(-2x^2 + 4x + 3) - 1)) + 2)/(1((-2(-2x^2 + 4x + 3) - 3)/(2(-2x^2 + 4x + 3) - 1)) + 1)) + 3| + 2 from x = 0.0 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
7.9
|
math
|
train
|
math_algebra_func_area_level_4_4_44
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1((-1(-3sin(3π(-1(-3|x + 3| - 2) + 3) + 3) - 2))/(2(-3sin(3π(-1(-3|x + 3| - 2) + 3) + 3) - 2) + 2))^2 + 1((-1(-3sin(3π(-1(-3|x + 3| - 2) + 3) + 3) - 2))/(2(-3sin(3π(-1(-3|x + 3| - 2) + 3) + 3) - 2) + 2)) and g(x) = 1cos(1π(-5(3|(5x^2 + 4x - 4) - 2| + 1)^2 - 4(3|(5x^2 + 4x - 4) - 2| + 1)) - 1) + 3 between the vertical lines x = -0.3 and x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.7
|
math
|
train
|
math_algebra_func_area_level_4_4_45
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2|((2((1(1cos(1π(2x - 3) - 2) + 2) + 2)/(-2(1cos(1π(2x - 3) - 2) + 2) - 1)) + 3)/(3((1(1cos(1π(2x - 3) - 2) + 2) + 2)/(-2(1cos(1π(2x - 3) - 2) + 2) - 1)) + 2)) + 1| - 3, g(x) = 2sin(3π(-1(-4(3x + 3)^2 - 1(3x + 3) - 2) + 1) - 2) - 2, x = -2.7, and x = -2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_46
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(4(-1|((-2(3|x - 3| + 1) - 1)/(2(3|x - 3| + 1) - 3)) + 3| - 2)^2 + 2(-1|((-2(3|x - 3| + 1) - 1)/(2(3|x - 3| + 1) - 3)) + 3| - 2)) - 2)/(2(4(-1|((-2(3|x - 3| + 1) - 1)/(2(3|x - 3| + 1) - 3)) + 3| - 2)^2 + 2(-1|((-2(3|x - 3| + 1) - 1)/(2(3|x - 3| + 1) - 3)) + 3| - 2)) + 2) and g(x) = 4((2(1sin(3π(-2|x + 1|) + 2) - 1) + 1)/(-2(1sin(3π(-2|x + 1|) + 2) - 1) + 1)) from x = 3.6 to x = 3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_4_4_47
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2(-1(-2sin(3π(-1|((1x - 2)/(-3x - 2)) + 2| + 1) + 2) + 2)^2 - 4(-2sin(3π(-1|((1x - 2)/(-3x - 2)) + 2| + 1) + 2) + 2) - 2) + 4 and g(x) = 3(-3(-2|(1x + 4) - 3| + 1)^2 + 4(-2|(1x + 4) - 3| + 1) + 5) - 1 between the vertical lines x = -2.0 and x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
79.4
|
math
|
train
|
math_algebra_func_area_level_4_4_48
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-2((-2(-1(1(-2x^2 - 1x - 4) + 5) + 3))/(-1(-1(1(-2x^2 - 1x - 4) + 5) + 3) - 1)) + 1)/(-1((-2(-1(1(-2x^2 - 1x - 4) + 5) + 3))/(-1(-1(1(-2x^2 - 1x - 4) + 5) + 3) - 1)) - 2) and g(x) = (3(3cos(3π((-2(-1x - 2) - 2)/(3(-1x - 2) - 2)) - 1) - 2) - 3)/(-3(3cos(3π((-2(-1x - 2) - 2)/(3(-1x - 2) - 2)) - 1) - 2) - 3) between the vertical lines x = -2.4 and x = -2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_4_4_49
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-1((2(-2e^(2(-2|(-3x^2 + 2x - 5)|)) + 1) - 1)/(3(-2e^(2(-2|(-3x^2 + 2x - 5)|)) + 1))) - 1)/(1((2(-2e^(2(-2|(-3x^2 + 2x - 5)|)) + 1) - 1)/(3(-2e^(2(-2|(-3x^2 + 2x - 5)|)) + 1))) + 3) and g(x) = 2cos(2π((3(-1(-3|x + 2| + 3) + 2) + 2)/(-3(-1(-3|x + 2| + 3) + 2))) - 1) - 1 between the vertical lines x = -2.1 and x = -1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_4_4_50
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2|(1(2(-2(1x + 3) - 4) - 1) - 1) + 1| - 3, g(x) = (1((3(2(-2e^(1x) + 3)^2 - 1(-2e^(1x) + 3) - 5))/(3(2(-2e^(1x) + 3)^2 - 1(-2e^(1x) + 3) - 5) - 1)) - 2)/(3((3(2(-2e^(1x) + 3)^2 - 1(-2e^(1x) + 3) - 5))/(3(2(-2e^(1x) + 3)^2 - 1(-2e^(1x) + 3) - 5) - 1)) - 2), x = -0.5, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
62.2
|
math
|
train
|
math_algebra_func_area_level_4_4_51
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3((-3(-2(5(-2|x - 2| + 2)^2 + 1(-2|x - 2| + 2) + 1) - 1))/(2(-2(5(-2|x - 2| + 2)^2 + 1(-2|x - 2| + 2) + 1) - 1) - 1))^2 + 4((-3(-2(5(-2|x - 2| + 2)^2 + 1(-2|x - 2| + 2) + 1) - 1))/(2(-2(5(-2|x - 2| + 2)^2 + 1(-2|x - 2| + 2) + 1) - 1) - 1)) + 5, g(x) = 4((-3(-2|(1x^2 - 2x - 4) + 2| - 1) + 2)/(2(-2|(1x^2 - 2x - 4) + 2| - 1) - 1))^2 + 2((-3(-2|(1x^2 - 2x - 4) + 2| - 1) + 2)/(2(-2|(1x^2 - 2x - 4) + 2| - 1) - 1)) - 2, x = -0.7, and x = 2.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.2
|
math
|
train
|
math_algebra_func_area_level_4_4_52
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -4(-2((3(-1|(3|x - 2| + 1) + 3| + 1) - 1)/(3(-1|(3|x - 2| + 1) + 3| + 1) + 1)))^2 + 5(-2((3(-1|(3|x - 2| + 1) + 3| + 1) - 1)/(3(-1|(3|x - 2| + 1) + 3| + 1) + 1))) + 3, g(x) = -4(2|(-1((3x + 1)/(-2x + 1))^2 + 1) + 1| - 3)^2 + 3(2|(-1((3x + 1)/(-2x + 1))^2 + 1) + 1| - 3) + 5, x = 0.1, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.6
|
math
|
train
|
math_algebra_func_area_level_4_4_53
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1(-2(-1(3|(1e^(1x)) - 2|)^2 + 4(3|(1e^(1x)) - 2|) + 3)^2 + 1(-1(3|(1e^(1x)) - 2|)^2 + 4(3|(1e^(1x)) - 2|) + 3) + 3)^2 + 2, g(x) = (-1(-1(3(-1|x - 1| - 3) - 3) - 5) - 2)/(-2(-1(3(-1|x - 1| - 3) - 3) - 5) + 3), x = -0.6, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.6
|
math
|
train
|
math_algebra_func_area_level_4_4_54
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3(1(-5(5(3|x - 3| - 2) + 4)^2 + 5(5(3|x - 3| - 2) + 4) + 5)^2 - 5(-5(5(3|x - 3| - 2) + 4)^2 + 5(5(3|x - 3| - 2) + 4) + 5) - 1) - 5, g(x) = 1(1((2(-3x^2 - 5x + 5))/(-2(-3x^2 - 5x + 5) - 2)) - 1)^2 - 3(1((2(-3x^2 - 5x + 5))/(-2(-3x^2 - 5x + 5) - 2)) - 1) - 3, x = 2.6, and x = 2.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
15.4
|
math
|
train
|
math_algebra_func_area_level_4_4_55
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -4(-2|(-2|(-5(1|x + 2|) - 2) - 2| - 1) - 3| + 2) - 4 and g(x) = 1|((2(2sin(1π(-1x - 1) - 1) - 2) + 1)/(-2(2sin(1π(-1x - 1) - 1) - 2) - 2)) - 1| + 3 between the vertical lines x = -1.5 and x = -1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
13.8
|
math
|
train
|
math_algebra_func_area_level_4_4_56
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (2(-4(-1(2(2x^2 + 4x - 2)^2 - 4(2x^2 + 4x - 2) - 1) - 4)^2 - 4(-1(2(2x^2 + 4x - 2)^2 - 4(2x^2 + 4x - 2) - 1) - 4) + 2) - 1)/(-3(-4(-1(2(2x^2 + 4x - 2)^2 - 4(2x^2 + 4x - 2) - 1) - 4)^2 - 4(-1(2(2x^2 + 4x - 2)^2 - 4(2x^2 + 4x - 2) - 1) - 4) + 2) + 1) and g(x) = (-2((3(1|(-5x^2 - 3x) - 3| + 2) - 2)/(-2(1|(-5x^2 - 3x) - 3| + 2) + 3)) - 2)/(3((3(1|(-5x^2 - 3x) - 3| + 2) - 2)/(-2(1|(-5x^2 - 3x) - 3| + 2) + 3)) + 2) from x = -2.6 to x = -2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_57
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2sin(1π((-3(-1(1|(-5x + 5) - 3| + 1)) - 3)/(-3(-1(1|(-5x + 5) - 3| + 1)))) + 2) - 1, g(x) = -4(3cos(2π(1(-1x^2) - 4) + 3) + 1) - 1, x = 2.3, and x = 2.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.4
|
math
|
train
|
math_algebra_func_area_level_4_4_58
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-3(2|(-5(-2(1e^(-1x) + 2) + 4)^2 - 4(-2(1e^(-1x) + 2) + 4) + 4) - 2| + 1))/(2(2|(-5(-2(1e^(-1x) + 2) + 4)^2 - 4(-2(1e^(-1x) + 2) + 4) + 4) - 2| + 1) + 2) and g(x) = -3((1(4(-1|x - 1| + 1)^2 - 3) + 1)/(2(4(-1|x - 1| + 1)^2 - 3)))^2 + 4((1(4(-1|x - 1| + 1)^2 - 3) + 1)/(2(4(-1|x - 1| + 1)^2 - 3))) - 2 from x = 1.4 to x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_4_4_59
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -3sin(3π((1(-3|(4(2|x - 3| - 2)^2 + 1(2|x - 3| - 2) + 1) + 1| - 1) + 3)/(2(-3|(4(2|x - 3| - 2)^2 + 1(2|x - 3| - 2) + 1) + 1| - 1) - 1)) - 2) + 2, g(x) = (2(1((3((-1x + 1)/(1x)) - 3)/(-3((-1x + 1)/(1x)) + 2)) + 1) + 1)/(1(1((3((-1x + 1)/(1x)) - 3)/(-3((-1x + 1)/(1x)) + 2)) + 1) - 3), x = 1.9, and x = 2.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_4_4_60
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-2(1(-2(2(-1|x - 2| - 2) - 3) + 3)^2 + 1) - 1)/(3(1(-2(2(-1|x - 2| - 2) - 3) + 3)^2 + 1) + 2) and g(x) = -1sin(2π(1((-3((-2x + 2)/(2x - 1)) - 2)/(2((-2x + 2)/(2x - 1)) + 3))^2 + 2((-3((-2x + 2)/(2x - 1)) - 2)/(2((-2x + 2)/(2x - 1)) + 3)) + 4) + 1) from x = -0.0 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_61
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 4(-1((-1(2(4x^2 - 5x + 4)^2 - 2(4x^2 - 5x + 4) + 3))/(1(2(4x^2 - 5x + 4)^2 - 2(4x^2 - 5x + 4) + 3) + 1)) - 5)^2 + 2(-1((-1(2(4x^2 - 5x + 4)^2 - 2(4x^2 - 5x + 4) + 3))/(1(2(4x^2 - 5x + 4)^2 - 2(4x^2 - 5x + 4) + 3) + 1)) - 5) and g(x) = 5((-3(-2e^(2(-3x^2 + 3x - 1)) + 1) - 2)/(-2(-2e^(2(-3x^2 + 3x - 1)) + 1) + 3))^2 + 3((-3(-2e^(2(-3x^2 + 3x - 1)) + 1) - 2)/(-2(-2e^(2(-3x^2 + 3x - 1)) + 1) + 3)) + 4 between the vertical lines x = -0.1 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
51.1
|
math
|
train
|
math_algebra_func_area_level_4_4_62
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1|((2(-4(-1|(1x^2 + 5x - 2) - 2|) + 5) - 1)/(-2(-4(-1|(1x^2 + 5x - 2) - 2|) + 5) + 3)) + 2| - 3, g(x) = -5(-1(2|(-3sin(3πx + 2) - 1) + 3| - 3)) + 1, x = -3.9, and x = -3.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
10.0
|
math
|
train
|
math_algebra_func_area_level_4_4_63
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1(-1|(4(-2(-1|x - 3| + 3) - 5) - 3) + 3| - 3) - 2)/(3(-1|(4(-2(-1|x - 3| + 3) - 5) - 3) + 3| - 3)), g(x) = (2(-3|(1e^(-2(2x - 2)) - 2) - 3| + 3) + 1)/(-1(-3|(1e^(-2(2x - 2)) - 2) - 3| + 3) - 3), x = 0.6, and x = 0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_64
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1(-2(-3(-2|((2x)/(-1x + 2)) - 3| - 1) - 1) + 2) - 1)/(3(-2(-3(-2|((2x)/(-1x + 2)) - 3| - 1) - 1) + 2) + 3), g(x) = (3((3((1(-2sin(3πx - 2) + 2) - 1)/(-2(-2sin(3πx - 2) + 2) - 2)) + 2)/(2((1(-2sin(3πx - 2) + 2) - 1)/(-2(-2sin(3πx - 2) + 2) - 2)) + 2)) - 2)/(-2((3((1(-2sin(3πx - 2) + 2) - 1)/(-2(-2sin(3πx - 2) + 2) - 2)) + 2)/(2((1(-2sin(3πx - 2) + 2) - 1)/(-2(-2sin(3πx - 2) + 2) - 2)) + 2)) - 2), x = -4.2, and x = -3.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_65
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2(4(-1(-2e^(2(2|x| - 3)) - 3)^2 - 5(-2e^(2(2|x| - 3)) - 3) + 1) - 2) and g(x) = -2cos(3π((-3(-1(1|x - 1| - 2) - 2) - 3)/(1(-1(1|x - 1| - 2) - 2) + 3))) - 2 from x = -1.5 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
146.1
|
math
|
train
|
math_algebra_func_area_level_4_4_66
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1(1cos(2π(2(-1(-3|x| - 1)^2 - 3) + 4) - 2) + 2)^2 - 5(1cos(2π(2(-1(-3|x| - 1)^2 - 3) + 4) - 2) + 2) - 4 and g(x) = -3|(3|(-2sin(1π(-1|x + 2| - 2)) + 2) - 3| - 3) + 3| + 3 from x = 3.4 to x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.7
|
math
|
train
|
math_algebra_func_area_level_4_4_67
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2(1sin(3π((-2(3(-2x^2 - 1x - 3)^2 - 5(-2x^2 - 1x - 3) - 4) + 1)/(3(3(-2x^2 - 1x - 3)^2 - 5(-2x^2 - 1x - 3) - 4) + 2)) + 1) - 2)^2 + 5(1sin(3π((-2(3(-2x^2 - 1x - 3)^2 - 5(-2x^2 - 1x - 3) - 4) + 1)/(3(3(-2x^2 - 1x - 3)^2 - 5(-2x^2 - 1x - 3) - 4) + 2)) + 1) - 2) - 4 and g(x) = 2(-3|(-3cos(2π(1|x + 2|) - 3)) - 1| - 2) between the vertical lines x = -0.2 and x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_4_4_68
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2sin(3π(-3|(-1|(5(-3x^2 + 1x + 4)^2 - 3) - 1| + 1) - 3| - 3) + 3), g(x) = 3(-1|(-1(2x + 3) + 3) - 3| + 3) + 3, x = -3.7, and x = -3.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_69
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-2(-1|((3(1(5x - 2) - 1) - 1)/(2(1(5x - 2) - 1) - 1)) - 2| + 1))/(-2(-1|((3(1(5x - 2) - 1) - 1)/(2(1(5x - 2) - 1) - 1)) - 2| + 1) - 3) and g(x) = -1sin(2π(-1(-3|((2x + 1)/(2x + 2)) + 2| - 2)^2 - 3(-3|((2x + 1)/(2x + 2)) + 2| - 2) - 5) + 2) + 1 between the vertical lines x = -2.0 and x = -1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_70
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1|((1(3|(2(-2x - 1)^2 + 1(-2x - 1) - 1) - 1| - 3) + 2)/(-3(3|(2(-2x - 1)^2 + 1(-2x - 1) - 1) - 1| - 3) - 1))| and g(x) = 3|((-3(-3|(2cos(2πx + 3) - 1) - 2| + 1) + 3)/(2(-3|(2cos(2πx + 3) - 1) - 2| + 1) + 2)) + 3| + 2 from x = -0.8 to x = -0.7000000000000001. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.1
|
math
|
train
|
math_algebra_func_area_level_4_4_71
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 4((-1(5(-2cos(3π((3x - 3)/(2x + 2))) + 3)^2 - 3(-2cos(3π((3x - 3)/(2x + 2))) + 3) - 5) + 2)/(-1(5(-2cos(3π((3x - 3)/(2x + 2))) + 3)^2 - 3(-2cos(3π((3x - 3)/(2x + 2))) + 3) - 5) - 1)) - 4 and g(x) = (-2(2|(1sin(2π(4x + 5)) + 3) + 2| - 1) + 2)/(1(2|(1sin(2π(4x + 5)) + 3) + 2| - 1) + 3) from x = -1.1 to x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.6
|
math
|
train
|
math_algebra_func_area_level_4_4_72
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1(1(2|(4(-1sin(2πx + 3) - 2)^2 - 2(-1sin(2πx + 3) - 2) - 1) - 2| - 2) - 3)^2 - 3(1(2|(4(-1sin(2πx + 3) - 2)^2 - 2(-1sin(2πx + 3) - 2) - 1) - 2| - 2) - 3) - 5 and g(x) = -1|((-3(2|(-2|x + 1| + 1) - 2|) - 3)/(-1(2|(-2|x + 1| + 1) - 2|) + 3)) - 2| between the vertical lines x = -1.8 and x = -1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_4_4_73
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1cos(1π(1|((2((-1((1x + 1)/(-3x + 4)) - 2)/(-3((1x + 1)/(-3x + 4)) - 3)))/(2((-1((1x + 1)/(-3x + 4)) - 2)/(-3((1x + 1)/(-3x + 4)) - 3)) - 1)) - 2| - 3) + 2) + 1, g(x) = (1((3(-1(-2x^2 - 5x + 5)) - 3)/(2(-1(-2x^2 - 5x + 5)) - 3)) + 1)/(-2((3(-1(-2x^2 - 5x + 5)) - 3)/(2(-1(-2x^2 - 5x + 5)) - 3))), x = 0.9, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_74
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3|(2(2sin(2π(-1(-5x^2 - 4x + 1)^2 + 4) + 3) + 2) + 4) + 1| - 1 and g(x) = -3(-3sin(2π(3(5x^2 - 4x + 1) - 5) - 3) - 3) + 5 from x = -0.6 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_4_4_75
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 4((3(2cos(3π((-2(1|x - 3| + 3) - 1)/(-3(1|x - 3| + 3) - 3)))))/(2(2cos(3π((-2(1|x - 3| + 3) - 1)/(-3(1|x - 3| + 3) - 3)))) + 1)) + 3, g(x) = 2(2|(1|(2x + 3) - 2| + 1) - 3| + 3)^2 - 2(2|(1|(2x + 3) - 2| + 1) - 3| + 3) - 5, x = 0.5, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_4_4_76
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2|(-4(4(3cos(3π(3x^2 - 1x - 3) + 3) + 1) + 5) - 5) - 3| + 3 and g(x) = -1sin(3π(-1|(5(3x^2 - 4x - 3)^2 - 4(3x^2 - 4x - 3) - 2) + 2| + 2)) + 3 from x = 2.1 to x = 2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
63.6
|
math
|
train
|
math_algebra_func_area_level_4_4_77
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -4(3(-2sin(2π(3|(-2x^2 + 2x + 1) - 3| - 3) - 1) - 1) - 3)^2 - 1(3(-2sin(2π(3|(-2x^2 + 2x + 1) - 3| - 3) - 1) - 1) - 3) and g(x) = 1(1(-1|(-3x + 3) + 2| + 3) + 1) + 2 between the vertical lines x = -0.4 and x = -0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
21.9
|
math
|
train
|
math_algebra_func_area_level_4_4_78
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 5(4((1((-1(5x^2 - 4x + 2) + 1)/(2(5x^2 - 4x + 2) - 3)) - 2)/(3((-1(5x^2 - 4x + 2) + 1)/(2(5x^2 - 4x + 2) - 3)) + 2)) + 4)^2 + 5(4((1((-1(5x^2 - 4x + 2) + 1)/(2(5x^2 - 4x + 2) - 3)) - 2)/(3((-1(5x^2 - 4x + 2) + 1)/(2(5x^2 - 4x + 2) - 3)) + 2)) + 4) + 3 and g(x) = -4(-2(-3cos(2π(1x^2 + 3x - 2) + 1) + 1)^2 + 2) - 3 from x = 0.4 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.2
|
math
|
train
|
math_algebra_func_area_level_4_4_79
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (3(-1|((-1(3((-1x + 1)/(-1x - 3))^2 - 3((-1x + 1)/(-1x - 3)) - 4) - 1)/(-1(3((-1x + 1)/(-1x - 3))^2 - 3((-1x + 1)/(-1x - 3)) - 4) - 1))| - 3) - 2)/(-2(-1|((-1(3((-1x + 1)/(-1x - 3))^2 - 3((-1x + 1)/(-1x - 3)) - 4) - 1)/(-1(3((-1x + 1)/(-1x - 3))^2 - 3((-1x + 1)/(-1x - 3)) - 4) - 1))| - 3) + 3) and g(x) = -5(3(2((-2x - 2)/(3x + 2))^2 - 5((-2x - 2)/(3x + 2)) - 4)^2 - 4)^2 + 1(3(2((-2x - 2)/(3x + 2))^2 - 5((-2x - 2)/(3x + 2)) - 4)^2 - 4) + 2 from x = 1.0 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.0
|
math
|
train
|
math_algebra_func_area_level_4_4_80
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 5(-2(-4(1(1|x + 3| - 1) + 1)^2 + 4(1(1|x + 3| - 1) + 1) + 1) + 4) + 4, g(x) = 1|(2(5(1cos(3πx - 3) - 1)^2 + 5(1cos(3πx - 3) - 1) - 5)^2 + 3(5(1cos(3πx - 3) - 1)^2 + 5(1cos(3πx - 3) - 1) - 5)) + 2| - 3, x = -4.2, and x = -4.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.5
|
math
|
train
|
math_algebra_func_area_level_4_4_81
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (2(2sin(3π(-2|(-4((-2x - 2)/(2x - 1))) - 2|)) + 1) - 1)/(3(2sin(3π(-2|(-4((-2x - 2)/(2x - 1))) - 2|)) + 1) + 1) and g(x) = -2(-2|(2(-3x - 4)^2 - 5(-3x - 4) + 2) + 3| + 2) - 2 between the vertical lines x = -1.4 and x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.3
|
math
|
train
|
math_algebra_func_area_level_4_4_82
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (2(-2(-1sin(1π(2|(5x^2 - 3x + 1) - 3| - 3) - 1))^2) - 2)/(1(-2(-1sin(1π(2|(5x^2 - 3x + 1) - 3| - 3) - 1))^2) + 3) and g(x) = 1(1(-2|(-3x - 2) - 1|) + 4)^2 + 5(1(-2|(-3x - 2) - 1|) + 4) - 2 between the vertical lines x = -2.5 and x = -2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_4_4_83
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (1((-3(-3|(-2sin(2π((-1x - 1)/(2x + 1)) - 1) + 1) + 2| + 3) - 1)/(1(-3|(-2sin(2π((-1x - 1)/(2x + 1)) - 1) + 1) + 2| + 3) - 2)) - 3)/(1((-3(-3|(-2sin(2π((-1x - 1)/(2x + 1)) - 1) + 1) + 2| + 3) - 1)/(1(-3|(-2sin(2π((-1x - 1)/(2x + 1)) - 1) + 1) + 2| + 3) - 2))), g(x) = 5(-2(-2|((-1x + 3)/(1x)) + 2|) - 1) - 4, x = -0.8, and x = -0.7000000000000001. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.8
|
math
|
train
|
math_algebra_func_area_level_4_4_84
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -4(1(-1(2(2|x - 1| - 3) - 5) - 3)^2 + 1(-1(2(2|x - 1| - 3) - 5) - 3) - 3)^2 - 3(1(-1(2(2|x - 1| - 3) - 5) - 3)^2 + 1(-1(2(2|x - 1| - 3) - 5) - 3) - 3) + 3 and g(x) = -2|(5(-2|(-1|x + 2| + 3) + 1|) + 2) - 1| + 1 between the vertical lines x = 2.6 and x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.1
|
math
|
train
|
math_algebra_func_area_level_4_4_85
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2(1(3e^(-1(3|(-2|x| - 3)| + 1)) + 1) + 2)^2 + 4(1(3e^(-1(3|(-2|x| - 3)| + 1)) + 1) + 2) - 5, g(x) = 4((2(1|(-1cos(2πx - 2) - 2) - 2|) + 2)/(-2(1|(-1cos(2πx - 2) - 2) - 2|) + 3))^2 - 4((2(1|(-1cos(2πx - 2) - 2) - 2|) + 2)/(-2(1|(-1cos(2πx - 2) - 2) - 2|) + 3)) + 1, x = -4.4, and x = -3.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.1
|
math
|
train
|
math_algebra_func_area_level_4_4_86
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3((2(-4(1((-1x - 3)/(2x - 1))^2 + 2((-1x - 3)/(2x - 1)) + 2)^2 - 4(1((-1x - 3)/(2x - 1))^2 + 2((-1x - 3)/(2x - 1)) + 2) + 3) - 2)/(2(-4(1((-1x - 3)/(2x - 1))^2 + 2((-1x - 3)/(2x - 1)) + 2)^2 - 4(1((-1x - 3)/(2x - 1))^2 + 2((-1x - 3)/(2x - 1)) + 2) + 3))) + 2 and g(x) = -3(-4(-3(4x - 4) - 1)^2 + 3(-3(4x - 4) - 1) + 1)^2 - 4(-4(-3(4x - 4) - 1)^2 + 3(-3(4x - 4) - 1) + 1) + 5 between the vertical lines x = 0.8 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_4_4_87
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2|(-1cos(2π((-2(2|(3|x - 3| + 3) + 2| + 2) - 3)/(-2(2|(3|x - 3| + 3) + 2| + 2) + 3)) + 1) + 2) - 1| - 2 and g(x) = (-1(2|(-1(-2|x + 3| - 1)^2 - 5(-2|x + 3| - 1) + 1) + 1| - 3))/(-2(2|(-1(-2|x + 3| - 1)^2 - 5(-2|x + 3| - 1) + 1) + 1| - 3) - 3) between the vertical lines x = -0.9 and x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.3
|
math
|
train
|
math_algebra_func_area_level_4_4_88
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1|(-1((3(-3|(-1x^2 + 4x + 2) - 2| + 1) + 3)/(1(-3|(-1x^2 + 4x + 2) - 2| + 1) - 2))^2 - 4((3(-3|(-1x^2 + 4x + 2) - 2| + 1) + 3)/(1(-3|(-1x^2 + 4x + 2) - 2| + 1) - 2)) + 4) - 2| + 2 and g(x) = (1(4((-2(5x^2 + 5) - 1)/(-3(5x^2 + 5) + 1))^2 + 2((-2(5x^2 + 5) - 1)/(-3(5x^2 + 5) + 1)) + 1) + 2)/(2(4((-2(5x^2 + 5) - 1)/(-3(5x^2 + 5) + 1))^2 + 2((-2(5x^2 + 5) - 1)/(-3(5x^2 + 5) + 1)) + 1) - 1) between the vertical lines x = 3.7 and x = 3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_89
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (2(-1|(3e^(1(5((1x - 3)/(2x - 1))^2 - 2((1x - 3)/(2x - 1)) + 4)) + 1) + 2|) - 3)/(-3(-1|(3e^(1(5((1x - 3)/(2x - 1))^2 - 2((1x - 3)/(2x - 1)) + 4)) + 1) + 2|) + 4), g(x) = -4(-2((-3((2x - 2)/(-2x - 2)) - 2)/(1((2x - 2)/(-2x - 2)) + 1))^2 - 2((-3((2x - 2)/(-2x - 2)) - 2)/(1((2x - 2)/(-2x - 2)) + 1)) + 3)^2 + 1(-2((-3((2x - 2)/(-2x - 2)) - 2)/(1((2x - 2)/(-2x - 2)) + 1))^2 - 2((-3((2x - 2)/(-2x - 2)) - 2)/(1((2x - 2)/(-2x - 2)) + 1)) + 3) + 2, x = 1.1, and x = 1.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.1
|
math
|
train
|
math_algebra_func_area_level_4_4_90
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2((2(-4(4(1x + 3) + 2)^2 - 3))/(-2(-4(4(1x + 3) + 2)^2 - 3) - 2)) - 5 and g(x) = -5(-4(-1|(2e^(1x)) - 2| + 1) + 1) - 4 between the vertical lines x = -0.4 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.0
|
math
|
train
|
math_algebra_func_area_level_4_4_91
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2(-2(-3|((-2(-1|x + 2| + 2) - 2)/(-1(-1|x + 2| + 2) + 2))| + 1) - 3)^2 - 5(-2(-3|((-2(-1|x + 2| + 2) - 2)/(-1(-1|x + 2| + 2) + 2))| + 1) - 3) - 3, g(x) = -4(-4(-3cos(2π(5x - 3) - 3)) - 1)^2 - 5, x = 4.2, and x = 4.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
27.7
|
math
|
train
|
math_algebra_func_area_level_4_4_92
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2(2|((-3(-5(2|x - 3| - 2) + 4) + 3)/(1(-5(2|x - 3| - 2) + 4))) - 3| + 3), g(x) = -1(-5(5(2|x + 2| - 3)) + 5), x = -3.0, and x = -1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
49.3
|
math
|
train
|
math_algebra_func_area_level_4_4_93
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 5((-2(-3e^(1(-3(-1|x| + 2)^2 + 1(-1|x| + 2) + 2)) + 2) + 1)/(-2(-3e^(1(-3(-1|x| + 2)^2 + 1(-1|x| + 2) + 2)) + 2) - 3))^2 - 1((-2(-3e^(1(-3(-1|x| + 2)^2 + 1(-1|x| + 2) + 2)) + 2) + 1)/(-2(-3e^(1(-3(-1|x| + 2)^2 + 1(-1|x| + 2) + 2)) + 2) - 3)) + 5 and g(x) = -4(-3|(3e^(1(1x^2 - 3x))) - 1| - 2) - 1 between the vertical lines x = -1.0 and x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
153.3
|
math
|
train
|
math_algebra_func_area_level_4_4_94
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (2(5((1((2(5x^2 + 3x - 3) - 2)/(-2(5x^2 + 3x - 3))) + 2)/(-1((2(5x^2 + 3x - 3) - 2)/(-2(5x^2 + 3x - 3))) - 3))^2 - 2) + 1)/(2(5((1((2(5x^2 + 3x - 3) - 2)/(-2(5x^2 + 3x - 3))) + 2)/(-1((2(5x^2 + 3x - 3) - 2)/(-2(5x^2 + 3x - 3))) - 3))^2 - 2) - 1), g(x) = (3(-2|(1|(-1x + 1) - 2| + 3) + 1| + 2) - 3)/(-1(-2|(1|(-1x + 1) - 2| + 3) + 1| + 2)), x = -1.2, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
7.4
|
math
|
train
|
math_algebra_func_area_level_4_4_95
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1(-3(-3cos(1π(3|(1x^2 - 5x) - 2| - 2) - 1) - 3) + 1), g(x) = 1(1(2(-3sin(2πx) + 1)^2 + 5(-3sin(2πx) + 1) - 3) + 3)^2 - 3(1(2(-3sin(2πx) + 1)^2 + 5(-3sin(2πx) + 1) - 3) + 3) - 4, x = -4.6, and x = -4.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_4_4_96
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3(-2sin(2π(2|(1(-3|x - 2| + 3)^2 + 4(-3|x - 2| + 3) - 5) + 1| - 1) - 2) + 1)^2 + 3(-2sin(2π(2|(1(-3|x - 2| + 3)^2 + 4(-3|x - 2| + 3) - 5) + 1| - 1) - 2) + 1) - 3 and g(x) = 1cos(3π((3((-2(2|x - 3|))/(2(2|x - 3|) + 3)) - 3)/(2((-2(2|x - 3|))/(2(2|x - 3|) + 3)) + 2)) - 2) - 2 between the vertical lines x = 4.6 and x = 4.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.8
|
math
|
train
|
math_algebra_func_area_level_4_4_97
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2sin(3π(2|(-4(-3|((-1x - 2)/(-2x)) - 1| - 2) - 5) - 1| - 1) - 2) - 2, g(x) = -1|(-4(5(3x + 1)^2 - 5(3x + 1) - 1)^2 - 1(5(3x + 1)^2 - 5(3x + 1) - 1)) + 1| + 2, x = -0.0, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_4_4_98
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1((-2(-4((-2((-3x + 2)/(2x - 1)) - 1)/(1((-3x + 2)/(2x - 1)) + 1)) + 1) - 1)/(1(-4((-2((-3x + 2)/(2x - 1)) - 1)/(1((-3x + 2)/(2x - 1)) + 1)) + 1))) - 3)/(-3((-2(-4((-2((-3x + 2)/(2x - 1)) - 1)/(1((-3x + 2)/(2x - 1)) + 1)) + 1) - 1)/(1(-4((-2((-3x + 2)/(2x - 1)) - 1)/(1((-3x + 2)/(2x - 1)) + 1)) + 1))) + 2), g(x) = (-3(4(2|(2e^(1x) - 2) + 1| - 2)^2 + 1(2|(2e^(1x) - 2) + 1| - 2) - 4) - 2)/(2(4(2|(2e^(1x) - 2) + 1| - 2)^2 + 1(2|(2e^(1x) - 2) + 1| - 2) - 4) + 2), x = 0.2, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_4_4_99
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2|(1(-3cos(2π(-1|(-2x + 4) - 2| - 1) - 2) - 2)^2 + 5(-3cos(2π(-1|(-2x + 4) - 2| - 1) - 2) - 2) + 4) + 3| - 2, g(x) = 1(4((2(-3cos(3πx + 1) - 2) + 3)/(3(-3cos(3πx + 1) - 2) - 2))^2 - 4((2(-3cos(3πx + 1) - 2) + 3)/(3(-3cos(3πx + 1) - 2) - 2)) + 1)^2 - 5(4((2(-3cos(3πx + 1) - 2) + 3)/(3(-3cos(3πx + 1) - 2) - 2))^2 - 4((2(-3cos(3πx + 1) - 2) + 3)/(3(-3cos(3πx + 1) - 2) - 2)) + 1) - 4, x = 3.7, and x = 3.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
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