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_2_2_0
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2e^(1(-1(-2|x| + 1)^2 - 5(-2|x| + 1) - 3)) - 1 and g(x) = (-3(-2x^2 - 4))/(-3(-2x^2 - 4) - 1) between the vertical lines x = -0.8 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.0
|
math
|
train
|
math_algebra_func_area_level_2_2_1
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1(-4(3x^2 - 4x + 1) + 3) + 3)/(2(-4(3x^2 - 4x + 1) + 3) + 1), g(x) = 5(-4x - 5) - 2, x = 0.0, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
54.4
|
math
|
train
|
math_algebra_func_area_level_2_2_2
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 5(-2(1sin(1πx - 1) - 1)^2 + 5(1sin(1πx - 1) - 1) - 1)^2 + 5(-2(1sin(1πx - 1) - 1)^2 + 5(1sin(1πx - 1) - 1) - 1) - 4 and g(x) = 1e^(2(-3x + 2)) - 2 from x = 4.7 to x = 4.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_2_2_3
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2sin(3π((-2(1x^2 - 1x - 4) + 1)/(2(1x^2 - 1x - 4) - 1))) and g(x) = (2(-1x^2 - 3x - 2) + 1)/(1(-1x^2 - 3x - 2)) between the vertical lines x = -2.4 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
64.5
|
math
|
train
|
math_algebra_func_area_level_2_2_4
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -4(-4(-3x^2 + 3x + 2) - 5)^2 - 3(-4(-3x^2 + 3x + 2) - 5) + 5 and g(x) = (2(1e^(-2x)) + 1)/(-1(1e^(-2x)) + 2) between the vertical lines x = -0.7 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.8
|
math
|
train
|
math_algebra_func_area_level_2_2_5
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-3(1(3e^(-1x) - 1)^2 - 3(3e^(-1x) - 1) + 2) + 2)/(2(1(3e^(-1x) - 1)^2 - 3(3e^(-1x) - 1) + 2) - 1), g(x) = 2e^(2((3x + 2)/(-1x + 3))) + 1, x = -0.1, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
15.2
|
math
|
train
|
math_algebra_func_area_level_2_2_6
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -4(2(4x) - 5)^2 - 1, g(x) = 2sin(2π(4x^2 - 4x - 4) + 3) - 3, x = 0.5, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_2_2_7
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3(-2(3sin(1πx - 2) - 2)^2 + 3(3sin(1πx - 2) - 2) + 2)^2 + 1(-2(3sin(1πx - 2) - 2)^2 + 3(3sin(1πx - 2) - 2) + 2) - 3 and g(x) = 3((-2x + 3)/(-3x)) - 4 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_2_2_8
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1(-2sin(2π(3x - 1) - 3) - 2)^2 - 3(-2sin(2π(3x - 1) - 3) - 2) + 2 and g(x) = 5(5x^2 + 3x - 1) - 4 from x = -1.4 to x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.4
|
math
|
train
|
math_algebra_func_area_level_2_2_9
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2|(-2sin(3π(-1x^2 - 1x + 4) - 1) - 2) - 2| + 3, g(x) = 5((-1x + 3)/(-3x - 3)) + 1, x = -2.1, and x = -2.0. 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_2_2_10
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2sin(3π(3|(-2|x| + 1) - 3| - 3) + 1) - 2 and g(x) = 2|(1x^2 - 2x - 3) - 2| - 3 from x = -1.6 to x = -1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_11
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(-1((-2x - 3)/(-1x))^2 + 2((-2x - 3)/(-1x))) + 3)/(1(-1((-2x - 3)/(-1x))^2 + 2((-2x - 3)/(-1x))) + 3) and g(x) = -5(3|x + 3|) + 3 from x = -3.2 to x = -2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_2_2_12
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -5(-1(3|x - 3| - 2)^2 - 4(3|x - 3| - 2) + 4) - 1, g(x) = (1(-2x - 4) + 2)/(3(-2x - 4) + 2), x = 2.0, and x = 4.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
52.9
|
math
|
train
|
math_algebra_func_area_level_2_2_13
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-3(5((3x)/(1x + 1))^2 + 1((3x)/(1x + 1))))/(3(5((3x)/(1x + 1))^2 + 1((3x)/(1x + 1))) - 1), g(x) = -1cos(3π(1x) + 2) - 1, x = 1.0, and x = 1.3. 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_2_2_14
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2sin(1π((2(2x^2 + 3x - 2))/(2(2x^2 + 3x - 2) + 2)) - 3) - 1 and g(x) = 1cos(2π((-1x + 2)/(1x)) + 2) + 1 from x = -0.2 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_2_2_15
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(-4(-1x - 2) - 2) - 3)/(2(-4(-1x - 2) - 2) + 1) and g(x) = 2sin(3π(2x - 1) + 3) + 1 from x = 2.3 to x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.6
|
math
|
train
|
math_algebra_func_area_level_2_2_16
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2(-3|(2sin(2πx - 1) - 2) + 1| + 3)^2 - 4(-3|(2sin(2πx - 1) - 2) + 1| + 3) - 4 and g(x) = 2|(-3|x - 1| + 2) + 3| - 2 between the vertical lines x = -2.9 and x = -2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
7.6
|
math
|
train
|
math_algebra_func_area_level_2_2_17
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (2(-3cos(1π((-2x - 2)/(-2x + 1)) - 3)) - 1)/(-3(-3cos(1π((-2x - 2)/(-2x + 1)) - 3)) - 2) and g(x) = (-2((2x + 3)/(-2x + 3)) - 1)/(3((2x + 3)/(-2x + 3)) + 3) from x = -1.6 to x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_2_2_18
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 3e^(1(-4(-1|x - 3| - 2)^2 - 5(-1|x - 3| - 2) - 3)) and g(x) = 1|(2cos(2πx - 1) + 1)| between the vertical lines x = -4.2 and x = -3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.4
|
math
|
train
|
math_algebra_func_area_level_2_2_19
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 4((2((-1x + 1)/(-2x - 1)) - 3)/(-3((-1x + 1)/(-2x - 1)) + 2)) - 2, g(x) = -3cos(1π(3x + 1) + 3) - 3, x = -0.8, and x = -0.5. 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_2_2_20
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2(2(1cos(3πx - 1))^2 + 2(1cos(3πx - 1)) - 2)^2 + 3(2(1cos(3πx - 1))^2 + 2(1cos(3πx - 1)) - 2) - 3 and g(x) = -4(4x^2 + 3x - 3) - 1 from x = 0.6 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_21
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 5(-3((-3x + 1)/(-2x + 3)) + 1) - 3 and g(x) = 5(-1cos(3πx + 2)) - 4 between the vertical lines x = -0.0 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_2_2_22
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-2(1|(1cos(3πx - 3) + 3) - 2| + 1) - 3)/(1(1|(1cos(3πx - 3) + 3) - 2| + 1) + 1) and g(x) = -1(2|x + 1|) - 2 from x = -1.2 to x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_2_2_23
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-3(-3|(3e^(2x) - 1) - 3|) - 1)/(1(-3|(3e^(2x) - 1) - 3|) - 3), g(x) = -1|(5x + 5) - 1|, x = -1.3, and x = -0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.0
|
math
|
train
|
math_algebra_func_area_level_2_2_24
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2cos(2π(5((1x - 2)/(2x - 3))^2 + 2((1x - 2)/(2x - 3)) - 1) - 3) - 2 and g(x) = -3(-2sin(1πx - 2) + 1)^2 + 1(-2sin(1πx - 2) + 1) + 2 between the vertical lines x = 1.2 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_25
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -5(1|(-2|x - 3|)| - 1), g(x) = -1|(-2cos(2πx - 3) + 2) - 1| + 2, x = 2.7, and x = 3.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.1
|
math
|
train
|
math_algebra_func_area_level_2_2_26
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-3(2|(2cos(2πx - 1) - 2)| - 3) + 3)/(-3(2|(2cos(2πx - 1) - 2)| - 3) - 3) and g(x) = -5(-1x + 3)^2 + 4(-1x + 3) + 3 from x = 4.0 to x = 4.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.3
|
math
|
train
|
math_algebra_func_area_level_2_2_27
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 4((1(3cos(3πx - 3) - 1) - 1)/(-1(3cos(3πx - 3) - 1) - 3)) + 3 and g(x) = (1(-2sin(1πx - 1) + 3) - 1)/(-3(-2sin(1πx - 1) + 3) + 4) between the vertical lines x = 0.6 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
18.8
|
math
|
train
|
math_algebra_func_area_level_2_2_28
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1(-1cos(1π((1x + 2)/(3x + 2)) - 2) - 1)^2 and g(x) = 2sin(3π((1x + 2)/(-2x - 2)) - 3) - 3 between the vertical lines x = -0.6 and x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_29
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2|(-1(-1cos(1πx - 1) - 1) - 5) + 2| + 3 and g(x) = 2e^(1(-1x + 2)) from x = 4.0 to x = 4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_2_2_30
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1((2((-1x)/(-3x - 1)) + 2)/(1((-1x)/(-3x - 1)))) + 2)/(-1((2((-1x)/(-3x - 1)) + 2)/(1((-1x)/(-3x - 1)))) - 3) and g(x) = 3cos(1π((-3x - 2)/(-1x - 2)) + 3) - 1 from x = -2.0 to x = -1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_31
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1(1((1x)/(2x + 2))^2 - 1((1x)/(2x + 2)) - 4)^2 - 5(1((1x)/(2x + 2))^2 - 1((1x)/(2x + 2)) - 4) and g(x) = 3|(3e^(-1x)) + 3| - 2 between the vertical lines x = -0.9 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
8.9
|
math
|
train
|
math_algebra_func_area_level_2_2_32
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3|(-2(1x^2 - 1x)) + 2| - 3, g(x) = 3e^(-1((3x - 1)/(-1x + 2))) - 2, x = -1.4, and x = -0.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
7.5
|
math
|
train
|
math_algebra_func_area_level_2_2_33
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (3((-1(-1|x + 1| + 1) - 3)/(-2(-1|x + 1| + 1) + 3)) - 1)/(2((-1(-1|x + 1| + 1) - 3)/(-2(-1|x + 1| + 1) + 3)) - 3) and g(x) = -1sin(2π((2x)/(-1x - 1))) from x = 0.1 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_2_2_34
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1(5(-3e^(-1x) + 1) + 1) - 1, g(x) = -2cos(2π(4x + 5) - 1) + 2, x = 0.5, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_35
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 3sin(3π(3(-1x - 4) + 3) + 1) - 3 and g(x) = -3(1|x| - 2)^2 - 3(1|x| - 2) + 4 between the vertical lines x = -2.8 and x = -2.6999999999999997. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_2_2_36
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-3(2cos(1π((2x)/(-1x - 1)) - 1) + 3) - 1)/(-2(2cos(1π((2x)/(-1x - 1)) - 1) + 3) + 3), g(x) = 3(-2e^(-2x) - 1), x = -0.4, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
16.9
|
math
|
train
|
math_algebra_func_area_level_2_2_37
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2(-3|((2x - 2)/(3x - 2)) - 2| + 3)^2 - 5(-3|((2x - 2)/(3x - 2)) - 2| + 3) - 1 and g(x) = 1sin(2π(-5x^2 - 1) + 3) + 1 from x = -0.5 to x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_38
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3e^(1(-1|(-1x + 5) + 1| - 3)), g(x) = 2|(-1x + 2)| - 1, x = 1.5, and x = 2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_2_2_39
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(3|(-3sin(1πx - 3) - 2) - 2| - 1))/(1(3|(-3sin(1πx - 3) - 2) - 2| - 1) - 3) and g(x) = -4(-1e^(1x) + 3)^2 + 4(-1e^(1x) + 3) - 3 from x = 0.3 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
10.0
|
math
|
train
|
math_algebra_func_area_level_2_2_40
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -3|((2(-2x^2 - 4x - 5) - 2)/(2(-2x^2 - 4x - 5) + 1)) + 1| + 3, g(x) = (2(-2x^2 + 4x - 1))/(-2(-2x^2 + 4x - 1) - 3), x = -0.2, and x = 2.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
15.3
|
math
|
train
|
math_algebra_func_area_level_2_2_41
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3(5(-4x^2 + 5x)^2 - 4)^2 + 3(5(-4x^2 + 5x)^2 - 4) - 1, g(x) = -3((2x + 2)/(2x + 2))^2 + 3, x = -0.1, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
6.0
|
math
|
train
|
math_algebra_func_area_level_2_2_42
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1sin(1π(1((-3x - 1)/(1x + 1))^2 + 3((-3x - 1)/(1x + 1)) - 3) - 3) - 1 and g(x) = 3|((1x)/(3x)) - 1| - 3 from x = -1.7 to x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_43
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3((-2(-2cos(3πx + 2) + 1) + 3)/(-2(-2cos(3πx + 2) + 1)))^2 - 5((-2(-2cos(3πx + 2) + 1) + 3)/(-2(-2cos(3πx + 2) + 1))) - 4 and g(x) = 2cos(1π(-3x) - 1) + 1 from x = 4.6 to x = 5.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.3
|
math
|
train
|
math_algebra_func_area_level_2_2_44
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3cos(3π(-1|(-3x + 5) - 1| + 1) + 2) - 2 and g(x) = (3(3sin(3πx - 3) + 3) - 3)/(-3(3sin(3πx - 3) + 3) - 3) from x = 4.6 to x = 4.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_2_2_45
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2|(-2e^(1((1x + 2)/(-1x))) - 1) - 2| - 3 and g(x) = (-2(2cos(1πx - 1) + 1) - 1)/(3(2cos(1πx - 1) + 1) + 2) between the vertical lines x = 1.1 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.5
|
math
|
train
|
math_algebra_func_area_level_2_2_46
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-2((1(3|x + 1| + 1) - 3)/(-1(3|x + 1| + 1) - 2)) - 1)/(-1((1(3|x + 1| + 1) - 3)/(-1(3|x + 1| + 1) - 2)) - 2) and g(x) = 1(2sin(1πx + 3) - 2)^2 - 2(2sin(1πx + 3) - 2) - 3 between the vertical lines x = 1.9 and x = 3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
15.6
|
math
|
train
|
math_algebra_func_area_level_2_2_47
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1|(-3|(2x - 5)| + 1) + 2| + 1 and g(x) = 4(-5x^2 - 1x + 2) + 5 from x = -1.4 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
37.9
|
math
|
train
|
math_algebra_func_area_level_2_2_48
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1(3sin(2π(-1x) - 1) - 3)^2 - 5(3sin(2π(-1x) - 1) - 3) + 4, g(x) = 3(-3cos(2πx + 1))^2 - 1(-3cos(2πx + 1)) + 4, x = -3.1, and x = -2.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
17.7
|
math
|
train
|
math_algebra_func_area_level_2_2_49
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1((2(-2|x| + 1) + 3)/(-1(-2|x| + 1) + 2))^2 + 4((2(-2|x| + 1) + 3)/(-1(-2|x| + 1) + 2)) - 1 and g(x) = -3|(-1|x + 1| + 2)| + 1 between the vertical lines x = -1.8 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
28.6
|
math
|
train
|
math_algebra_func_area_level_2_2_50
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3(-2(4x^2 + 2x - 2) - 1) - 1 and g(x) = 1|(2cos(1πx + 2) + 2)| - 1 from x = -0.8 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
6.4
|
math
|
train
|
math_algebra_func_area_level_2_2_51
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3(2|(5x^2 - 5x - 4) - 1| - 2)^2 - 5(2|(5x^2 - 5x - 4) - 1| - 2) - 3, g(x) = 3|(-5x + 1)| - 2, x = -0.6, and x = -0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.9
|
math
|
train
|
math_algebra_func_area_level_2_2_52
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-2(2cos(3π(1x + 2) + 1)) + 3)/(1(2cos(3π(1x + 2) + 1))), g(x) = 2(-4x^2 - 3)^2 + 5(-4x^2 - 3) - 1, x = -0.6, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
8.6
|
math
|
train
|
math_algebra_func_area_level_2_2_53
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1(5(-2|x - 1| + 3) + 1)^2 + 3(5(-2|x - 1| + 3) + 1) and g(x) = -3cos(2π((-2x - 2)/(1x - 2))) - 2 from x = 2.9 to x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_2_2_54
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(3sin(1π((2x - 2)/(1x - 2)) - 2) + 1) - 2)/(3(3sin(1π((2x - 2)/(1x - 2)) - 2) + 1) + 2) and g(x) = 1|((-2x - 1)/(-2x + 3)) + 2| from x = 2.2 to x = 2.3000000000000003. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.6
|
math
|
train
|
math_algebra_func_area_level_2_2_55
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1|(1e^(1(2|x - 2|)) - 3) - 2| + 2, g(x) = (-1((2x)/(-1x - 1)) + 3)/(1((2x)/(-1x - 1))), x = 0.0, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
38.5
|
math
|
train
|
math_algebra_func_area_level_2_2_56
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (3(3|(2sin(3πx + 1) - 3) + 3| - 2) + 3)/(1(3|(2sin(3πx + 1) - 3) + 3| - 2) + 2) and g(x) = -2cos(1π(1x - 5) + 2) - 3 from x = 2.9 to x = 3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.2
|
math
|
train
|
math_algebra_func_area_level_2_2_57
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(-3(-5x^2 + 4x - 2) - 5) + 1)/(1(-3(-5x^2 + 4x - 2) - 5) + 1) and g(x) = -2(-3x^2 - 2x) + 1 from x = 0.1 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
23.3
|
math
|
train
|
math_algebra_func_area_level_2_2_58
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-1(-1|(5x + 2) - 2| + 3) - 2)/(-2(-1|(5x + 2) - 2| + 3) + 3) and g(x) = 3(3x^2 + 5x - 5) - 5 between the vertical lines x = -2.6 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
49.8
|
math
|
train
|
math_algebra_func_area_level_2_2_59
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (2(-2|(1cos(1πx + 1) - 3) + 2| + 3) + 1)/(1(-2|(1cos(1πx + 1) - 3) + 2| + 3) - 3), g(x) = -3|(1e^(2x) + 2) + 2| + 3, x = -0.1, and x = 1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
42.8
|
math
|
train
|
math_algebra_func_area_level_2_2_60
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1|((-3(3e^(1x) - 3) - 3)/(-1(3e^(1x) - 3) - 2)) - 2| + 1 and g(x) = 3(2cos(3πx + 1) + 2)^2 - 3(2cos(3πx + 1) + 2) from x = -5.0 to x = -4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
6.3
|
math
|
train
|
math_algebra_func_area_level_2_2_61
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3|(-1cos(2π(-4x - 3) - 1)) + 2| + 1, g(x) = 2(2x - 4) + 2, x = 3.3, and x = 3.4. 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_2_2_62
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-2(-3|((-3x + 3)/(-1x + 2)) - 2| + 3) + 2)/(-2(-3|((-3x + 3)/(-1x + 2)) - 2| + 3) + 1), g(x) = -2e^(1(1x + 2)) + 2, x = -2.4, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
22.8
|
math
|
train
|
math_algebra_func_area_level_2_2_63
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1cos(2π(-3(-1x - 4)^2 - 3)) + 1, g(x) = 3(-1e^(1x) + 2)^2 + 5(-1e^(1x) + 2) - 3, x = 0.4, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.2
|
math
|
train
|
math_algebra_func_area_level_2_2_64
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1(1|((-2x - 1)/(3x)) + 3| + 3) - 3)/(-1(1|((-2x - 1)/(3x)) + 3| + 3) - 2), g(x) = 1(1x^2 + 5x + 2) + 2, x = -4.3, and x = -0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
8.3
|
math
|
train
|
math_algebra_func_area_level_2_2_65
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2e^(1((-1(-1x - 5) - 2)/(1(-1x - 5)))) + 1 and g(x) = 3(4x^2 - 4x - 1) between the vertical lines x = -0.2 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.6
|
math
|
train
|
math_algebra_func_area_level_2_2_66
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -5(-2(1x^2 - 4x + 5) - 1) + 2 and g(x) = 2(3|x - 3| - 3)^2 - 4(3|x - 3| - 3) - 2 between the vertical lines x = -0.5 and x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
53.7
|
math
|
train
|
math_algebra_func_area_level_2_2_67
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (3(-2|(-3x + 4) - 3| - 2) - 2)/(3(-2|(-3x + 4) - 3| - 2) - 2) and g(x) = -1((1x + 1)/(-2x - 1))^2 - 1((1x + 1)/(-2x - 1)) + 4 between the vertical lines x = -0.6 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.8
|
math
|
train
|
math_algebra_func_area_level_2_2_68
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1(1|(5x^2 - 4x + 1) - 2| - 1)^2 + 2(1|(5x^2 - 4x + 1) - 2| - 1), g(x) = 2e^(-1(2x^2 + 5x + 5)) + 3, x = -0.5, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.3
|
math
|
train
|
math_algebra_func_area_level_2_2_69
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3(-1(-1x)) + 4, g(x) = -4(3e^(-1x) - 3)^2 + 5(3e^(-1x) - 3) + 2, x = -0.3, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_2_2_70
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-1(2cos(2π(1x^2 - 2x - 3) - 2) + 3) - 3)/(2(2cos(2π(1x^2 - 2x - 3) - 2) + 3) - 1) and g(x) = -5((-1x + 2)/(2x - 1))^2 + 1((-1x + 2)/(2x - 1)) + 5 between the vertical lines x = -0.7 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_71
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3cos(2π(2|(1x - 4) - 3| - 3) - 1) - 1 and g(x) = -3cos(3π(2|x - 2| - 2) + 1) - 3 from x = -2.2 to x = -2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_2_2_72
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 4(-2sin(2π((1x - 3)/(-1x - 1)) + 3) + 3) + 1, g(x) = (1(2x^2 - 4x - 5) - 3)/(-3(2x^2 - 4x - 5) - 1), x = -0.8, and x = -0.7000000000000001. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.6
|
math
|
train
|
math_algebra_func_area_level_2_2_73
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-3(2|(2cos(3πx + 1) + 3) - 2|) + 2)/(1(2|(2cos(3πx + 1) + 3) - 2|) + 1) and g(x) = 3cos(1π((-1x - 3)/(1x - 2)) + 1) - 1 between the vertical lines x = 1.9 and x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_74
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-2(-4(2cos(1πx - 3) - 2)^2 + 1(2cos(1πx - 3) - 2) - 4) - 1)/(2(-4(2cos(1πx - 3) - 2)^2 + 1(2cos(1πx - 3) - 2) - 4) + 2) and g(x) = -3sin(1π(2|x + 2| + 2)) - 1 between the vertical lines x = 4.0 and x = 4.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_2_2_75
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3sin(3π(3|(1x^2 - 3x - 3) + 3| + 1) + 2) + 2, g(x) = 1(-1|x + 2|)^2 - 4(-1|x + 2|) + 4, x = -2.0, and x = -1.9. 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_2_2_76
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3sin(2π(2(1x - 4) - 1) - 1) - 3, g(x) = (1(-1|x + 2| - 1) + 3)/(-1(-1|x + 2| - 1) + 2), x = 3.8, and x = 4.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.3
|
math
|
train
|
math_algebra_func_area_level_2_2_77
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -5(3(3|x - 3| - 2)^2 - 2(3|x - 3| - 2) - 3) + 1 and g(x) = -5(2sin(3πx - 3) - 1)^2 + 5(2sin(3πx - 3) - 1) + 1 between the vertical lines x = 3.3 and x = 4.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
31.9
|
math
|
train
|
math_algebra_func_area_level_2_2_78
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1(-3(-2|x - 1| + 2)^2 - 4(-2|x - 1| + 2) + 3)^2 + 5 and g(x) = (-2(1x) - 2)/(2(1x)) from x = 2.7 to x = 3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.5
|
math
|
train
|
math_algebra_func_area_level_2_2_79
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-1(-2(-1x - 2)^2 - 4(-1x - 2)) + 3)/(-3(-2(-1x - 2)^2 - 4(-1x - 2)) + 2) and g(x) = (1(2sin(1πx)) + 1)/(-2(2sin(1πx)) + 3) between the vertical lines x = 1.0 and x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_2_2_80
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3|(-3sin(2π(-5x - 1) - 1) - 3) + 1| - 2 and g(x) = -1|((2x - 3)/(1x - 3)) - 1| + 1 between the vertical lines x = 3.8 and x = 3.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_2_2_81
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2|(-3cos(1π(4x^2 + 1x - 3) - 1) - 2)| + 2 and g(x) = (-3(-1x - 2) - 3)/(2(-1x - 2) - 1) from x = -4.6 to x = -4.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_2_2_82
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2|((-1(-3x^2 + 1) - 2)/(-2(-3x^2 + 1) - 1)) + 1| - 2 and g(x) = (-3(-3x^2 + 5x - 4) + 2)/(-1(-3x^2 + 5x - 4) + 3) from x = 0.0 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
6.4
|
math
|
train
|
math_algebra_func_area_level_2_2_83
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-3(-2sin(1π(-2|x + 2| + 3) - 3)) + 2)/(-1(-2sin(1π(-2|x + 2| + 3) - 3)) + 3) and g(x) = 1(-1e^(-2x) - 3)^2 + 3(-1e^(-2x) - 3) + 1 from x = 3.6 to x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_84
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2|(3(-4x - 1) + 1) - 3| + 3 and g(x) = -2sin(1π(-2x - 5)) - 3 between the vertical lines x = -0.8 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.4
|
math
|
train
|
math_algebra_func_area_level_2_2_85
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2cos(1π(3(3|x - 2|) - 1) - 2) - 2, g(x) = -3(4x + 2), x = -0.4, and x = -0.2. 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_2_2_86
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 3(-2sin(3π((-2x - 2)/(2x - 1)) - 3) + 1)^2 - 3(-2sin(3π((-2x - 2)/(2x - 1)) - 3) + 1) - 4 and g(x) = 1|(1|x - 3| + 1) + 3| + 1 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}"
]
}
|
0.8
|
math
|
train
|
math_algebra_func_area_level_2_2_87
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-1(-2(-5x^2 + 3x + 2) + 2) - 2)/(-3(-2(-5x^2 + 3x + 2) + 2) - 3) and g(x) = (-3(-2sin(1πx + 3) + 1) + 2)/(2(-2sin(1πx + 3) + 1) - 3) between the vertical lines x = -0.9 and x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.8
|
math
|
train
|
math_algebra_func_area_level_2_2_88
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1(-5(-2cos(1πx + 3) - 2) - 1) + 1 and g(x) = 2sin(3π(-3|x - 3| - 2) - 2) - 1 from x = 0.0 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
22.1
|
math
|
train
|
math_algebra_func_area_level_2_2_89
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1((-2(-1|x - 3| - 1) - 3)/(2(-1|x - 3| - 1))) + 1, g(x) = -3(5x^2 - 3x - 4) - 5, x = -0.4, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
6.1
|
math
|
train
|
math_algebra_func_area_level_2_2_90
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1(-3((3x + 1)/(2x))^2 + 4((3x + 1)/(2x)) + 1)^2 + 5(-3((3x + 1)/(2x))^2 + 4((3x + 1)/(2x)) + 1) - 3 and g(x) = -5(-3|x|) - 4 between the vertical lines x = -0.5 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_91
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-3(4(-4x^2 + 2x + 2) + 2) + 3)/(2(4(-4x^2 + 2x + 2) + 2) - 1), g(x) = -2cos(3π(-4x + 1) + 1) - 3, x = 3.7, and x = 3.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_92
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-3(-1|(2|x - 2|) + 1| + 3) + 3)/(-2(-1|(2|x - 2|) + 1| + 3) + 3) and g(x) = 2(3x^2 + 4x + 4) + 5 between the vertical lines x = 1.8 and x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
19.4
|
math
|
train
|
math_algebra_func_area_level_2_2_93
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(-2|(4x - 2) + 3| + 3))/(3(-2|(4x - 2) + 3| + 3) + 3) and g(x) = 2|(-3e^(1x) - 3) - 3| + 2 from x = -0.8 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
20.5
|
math
|
train
|
math_algebra_func_area_level_2_2_94
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 4(1|((-2x + 1)/(2x - 3))| + 3)^2 + 2(1|((-2x + 1)/(2x - 3))| + 3) + 3 and g(x) = 2e^(2(-3x^2 - 4x + 1)) + 1 between the vertical lines x = -1.1 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
82.5
|
math
|
train
|
math_algebra_func_area_level_2_2_95
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1(-5(3cos(3πx - 1) + 1) - 5)^2 - 2(-5(3cos(3πx - 1) + 1) - 5) + 4 and g(x) = (-1((2x + 2)/(2x + 2)) + 3)/(1((2x + 2)/(2x + 2)) + 1) between the vertical lines x = 3.0 and x = 3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.4
|
math
|
train
|
math_algebra_func_area_level_2_2_96
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1(1sin(3π(3x^2 - 3x + 1)) - 3)^2 - 2(1sin(3π(3x^2 - 3x + 1)) - 3) + 5 and g(x) = 4(1x - 2)^2 + 3(1x - 2) + 2 between the vertical lines x = 2.5 and x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_2_2_97
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2|((-1(1|x - 3| - 2))/(2(1|x - 3| - 2) + 2)) + 1| - 3 and g(x) = (2(3x - 5) + 2)/(1(3x - 5) - 3) between the vertical lines x = 1.4 and x = 3.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
87.7
|
math
|
train
|
math_algebra_func_area_level_2_2_98
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2|(-1|(4x^2 + 2x) + 2| + 2) + 2| - 3 and g(x) = (1(-2|x + 1|) + 1)/(2(-2|x + 1|) - 1) between the vertical lines x = 0.2 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_2_2_99
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (3((1(-2|x + 2| + 2) - 3)/(3(-2|x + 2| + 2) - 1)) + 3)/(-2((1(-2|x + 2| + 2) - 3)/(3(-2|x + 2| + 2) - 1)) + 1) and g(x) = 3cos(3π(-4x - 5) + 2) - 3 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}"
]
}
|
0.2
|
math
|
train
|
End of preview. Expand
in Data Studio
README.md exists but content is empty.
- Downloads last month
- 17