

'''simple docstring'''

from collections.abc import Callable

import numpy as np




def 							_UpperCamelCase				(   lowerCAmelCase__:					Callable		,lowerCAmelCase__:					float		,lowerCAmelCase__:					float		,lowerCAmelCase__:					float		,lowerCAmelCase__:					float   )      -> np.ndarray:
							SCREAMING_SNAKE_CASE_				=				int(np.ceil((x_end - xa) / step_size   )   )
							SCREAMING_SNAKE_CASE_				=				np.zeros((n + 1,)   )
							SCREAMING_SNAKE_CASE_				=				ya
							SCREAMING_SNAKE_CASE_				=				xa

							for k in range(__lowerCamelCase   ):
														SCREAMING_SNAKE_CASE_				=				y[k] + step_size * ode_func(__lowerCamelCase		,y[k]   )
														x += step_size

							return y


if __name__ == "__main__":
							import doctest

							doctest.testmod()










def        __lowerCAmelCase		(	__lowerCamelCase						:     int					, __lowerCamelCase						:     int						)	->    bool:
					return numa ^ numa < 0


if __name__ == "__main__":
				import doctest

				doctest.testmod()




