






"""simple docstring"""






from collections.abc import Callable

import numpy as np



def  __lowerCamelCase					(					lowerCAmelCase__       ,lowerCAmelCase__       ,lowerCAmelCase__       ,lowerCAmelCase__       ,lowerCAmelCase__				):
				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]				)
								x += step_size

				return y


if __name__ == "__main__":
					import doctest

					doctest.testmod()










"""simple docstring"""






from math import factorial, pi



def  __lowerCamelCase					(					lowerCAmelCase__       ,lowerCAmelCase__ = 30				):

				if not isinstance(lowerCAmelCase__       ,(int, float)				):
								raise ValueError('maclaurin_sin() requires either an int or float for theta'				)

				if not isinstance(lowerCAmelCase__       ,lowerCAmelCase__				) or accuracy <= 0:
								raise ValueError('maclaurin_sin() requires a positive int for accuracy'				)

				A__							 =       float(lowerCAmelCase__				)
				A__							 =       theta // (2 * pi)
				theta -= 2 * div * pi
				return sum(
				    (-1) ** r * theta ** (2 * r + 1) / factorial(2 * r + 1				) for r in range(lowerCAmelCase__				)				)



def  __lowerCamelCase					(					lowerCAmelCase__       ,lowerCAmelCase__ = 30				):

				if not isinstance(lowerCAmelCase__       ,(int, float)				):
								raise ValueError('maclaurin_cos() requires either an int or float for theta'				)

				if not isinstance(lowerCAmelCase__       ,lowerCAmelCase__				) or accuracy <= 0:
								raise ValueError('maclaurin_cos() requires a positive int for accuracy'				)

				A__							 =       float(lowerCAmelCase__				)
				A__							 =       theta // (2 * pi)
				theta -= 2 * div * pi
				return sum((-1) ** r * theta ** (2 * r) / factorial(2 * r				) for r in range(lowerCAmelCase__				)				)


if __name__ == "__main__":
					import doctest

					doctest.testmod()

					print(maclaurin_sin(10))
					print(maclaurin_sin(-10))
					print(maclaurin_sin(10, 15))
					print(maclaurin_sin(-10, 15))

					print(maclaurin_cos(5))
					print(maclaurin_cos(-5))
					print(maclaurin_cos(10, 15))
					print(maclaurin_cos(-10, 15))


