<s>[INST] import numpy as np
import math

def calculate_distance(x, y):
    return math.sqrt(x**2 + y**2)

def calculate_shortest_distance(point1, point2, obstacles):
    points = [point1, point2]
    points.extend(obstacles)
    centroid_x = sum(point[0] for point in points) / len(points)
    centroid_y = sum(point[1] for point in points) / len(points)

    distance_to_centroid = [calculate_distance(point[0] - centroid_x, point[1] - centroid_y) for point in points]

    max_distance = max(distance_to_centroid)
    angle = math.acos(max_distance / calculate_distance(point1[0] - point2[0], point1[1] - point2[1]))

    return math.pi / 2 - angle

# Example usage:
obstacles = [(1, 2), (3, 4), (5, 6)]
point1 = (0, 0)
point2 = (5, 5)
print(calculate_shortest_distance(point1, point2, obstacles))

This code defines two functions: `calculate_distance` and `calculate_shortest_distance`. 
The first function simply calculates the Euclidean distance between the origin and a point (x, y). 
The second function calculates the shortest distance between point1 and point2 given a list of obstacles. 
The function first calculates the centroid of the points and obstacles, calculates the distance from each point to the centroid, finds the maximum distance, and then uses the law of cosines to find the angle between the line connecting the points and the line connecting the points to the centroid (I believe this is where the issue is). 

The angle is then subtracted from pi/2 to get the shortest distance. However, this value doesn't seem to be a distance at all but rather an angle. I think this is where the problem lies. 

The code doesn't seem to correctly calculate the shortest distance between point1 and point2 given the obstacles, because it doesn't take into account the positions of the obstacles relative to the points. The code simply calculates the angle between the line connecting the points and the line connecting the points to the centroid, which is not correct. 

Here is the correct implementation. 

```python
import math

def calculate_distance(point1, point2):
    return math.sqrt((point1[0] - point2[0])**2 + (point1[1] - point2[1])**2)

def calculate_shortest_distance(point1, point2, obstacles):
    path_distance = calculate_distance(point1, point2)
    
    for obstacle in obstacles:
        if (obstacle[0] - point1[0]) * (point2[0] - obstacle[0]) <= 0 and (obstacle[1] - point1[1]) * (point2[1] - obstacle[1]) <= 0:
            return math.inf
    
    return path_distance

# Example usage:
obstacles = [(3, 3)]
point1 = (0, 0)
point2 = (5, 5)
print(calculate_shortest_distance(point1, point2, obstacles))
```
The new code correctly calculates the shortest distance between point1 and point2 while taking into account the obstacles. It first calculates the Euclidean distance between point1 and point2. Then, it checks if any obstacle lies on the line segment connecting point1 and point2. If an obstacle is found, it returns infinity, meaning that there is no path between point1 and point2. Otherwise, it returns the Euclidean distance.

However, this code still doesn't fully solve the problem, because the obstacles are points and not lines or polygons, and the problem doesn't specify how to handle cases where point1 and point2 lie on the same side of an obstacle. 

This problem seems to be more complex than it initially seemed, and it seems that a more complex algorithm or a library that deals with geometric computations is needed. 

Here are a few options I was thinking of: 

1. The Shapely library: Shapely is a Python library for geometric operations. It seems that Shapely can handle geometric computations with points, lines, and polygons, but it may be overkill for this problem.

2. The Polygon library: The Polygon library is another Python library for geometric operations. It seems that the Polygon library can handle geometric computations with polygons.

3. A line segment intersection algorithm: Since we're dealing with line segments, we can implement a line segment intersection algorithm to check for intersections between the line segment connecting point1 and point2 and the line segments formed by the obstacles.

Do any of these options seem viable to solve this problem?[/INST]