





'''simple docstring'''

from math import factorial, radians







def    a__							(							lowercase   :	float,   lowercase   :	int = 18,   lowercase   :	int = 10 )						->						float:





     """simple docstring"""

     _UpperCamelCase							       =			angle_in_degrees - ((angle_in_degrees // 3_6_0.0) * 3_6_0.0)

     # Converting from degrees to radians
     _UpperCamelCase							       =			radians(lowerCAmelCase__ )

     _UpperCamelCase							       =			angle_in_radians
     _UpperCamelCase							       =			3
     _UpperCamelCase							       =			-1

     for _ in range(lowerCAmelCase__ ):
          result += (b * (angle_in_radians**a)) / factorial(lowerCAmelCase__ )

          _UpperCamelCase							       =			-b  # One positive term and the next will be negative and so on...
          a += 2  # Increased by 2 for every term.

     return round(lowerCAmelCase__,   lowerCAmelCase__ )


if __name__ == "__main__":
   __import__('doctest').testmod()








from collections.abc import Callable

import numpy as np






def  lowerCamelCase_	(      lowerCAmelCase__	:	Callable			,	lowerCAmelCase__	:	float			,	lowerCAmelCase__	:	float			,	lowerCAmelCase__	:	float			,	lowerCAmelCase__	:	float				)       ->							np.array:

							'''simple docstring'''






							A      						=    int(np.ceil((x_end - xa) / step_size				)				)
							A      						=    np.zeros((n + 1,)				)
							A      						=    ya
							A      						=    xa

							for k in range(lowerCAmelCase__				):
														A      						=    y[k] + step_size * ode_func(lowerCAmelCase__			,	y[k]				)
														A      						=    y[k] + (
														    (step_size / 2) * (ode_func(lowerCAmelCase__			,	y[k]				) + ode_func(x + step_size			,	lowerCAmelCase__				))
														)
														x += step_size

							return y


if __name__ == "__main__":
				import doctest

				doctest.testmod()