




'''simple docstring'''



from __future__ import annotations

from numpy import array, cos, cross, floataa, radians, sin
from numpy.typing import NDArray







def       _UpperCamelCase			(_lowerCamelCase				:  float ,						_lowerCamelCase				:  float ,						_lowerCamelCase				:  bool = False						)-> list[float]:




     '''simple docstring'''





     if radian_mode:
          return [magnitude * cos(_lowerCamelCase						), magnitude * sin(_lowerCamelCase						)]
     return [magnitude * cos(radians(_lowerCamelCase						)						), magnitude * sin(radians(_lowerCamelCase						)						)]







def       _UpperCamelCase			(_lowerCamelCase				:  NDArray[floataa] ,						_lowerCamelCase				:  NDArray[floataa] ,						_lowerCamelCase				:  float = 10**-1						)-> bool:




     '''simple docstring'''





     __snake_case            =	cross(_lowerCamelCase ,						_lowerCamelCase						)
     __snake_case            =	sum(_lowerCamelCase						)
     return abs(_lowerCamelCase						) < eps


if __name__ == "__main__":
     # Test to check if it works
     UpperCAmelCase_							:	List[str]	     =		array(
         [
             polar_force(718.4, 1_8_0 - 3_0),
             polar_force(879.54, 4_5),
             polar_force(1_0_0, -9_0),
         ]
     )

     UpperCAmelCase_							:	NDArray[floataa]	     =		array([[0, 0], [0, 0], [0, 0]])

     assert in_static_equilibrium(forces, location)

     # Problem 1 in image_data/2D_problems.jpg
     UpperCAmelCase_							:	str	     =		array(
         [
             polar_force(3_0 * 9.81, 1_5),
             polar_force(2_1_5, 1_8_0 - 4_5),
             polar_force(2_6_4, 9_0 - 3_0),
         ]
     )

     UpperCAmelCase_							:	Optional[Any]	     =		array([[0, 0], [0, 0], [0, 0]])

     assert in_static_equilibrium(forces, location)

     # Problem in image_data/2D_problems_1.jpg
     UpperCAmelCase_							:	List[Any]	     =		array([[0, -2_0_0_0], [0, -1_2_0_0], [0, 1_5_6_0_0], [0, -1_2_4_0_0]])

     UpperCAmelCase_							:	int	     =		array([[0, 0], [6, 0], [1_0, 0], [1_2, 0]])

     assert in_static_equilibrium(forces, location)

     import doctest

     doctest.testmod()












'''simple docstring'''



def       _UpperCamelCase			(_lowerCamelCase				:  int ,						_lowerCamelCase				:  int ,						_lowerCamelCase				:  int						)-> float:




     '''simple docstring'''





     __snake_case            =	(num_of_terms / 2) * (2 * first_term + (num_of_terms - 1) * common_diff)
     # formula for sum of series
     return total







def       _UpperCamelCase			()-> str:




     '''simple docstring'''





     print(sum_of_series(1 ,						1 ,						10						)						)


if __name__ == "__main__":
     import doctest

     doctest.testmod()






