



"""simple docstring"""






from collections.abc import Callable

import numpy as np






def   snake_case__     (	__lowerCamelCase       :					Callable							,	__lowerCamelCase       :					float							,	__lowerCamelCase       :					float							,	__lowerCamelCase       :					float							,	__lowerCamelCase       :					float			):
			"""simple docstring"""
			lowerCamelCase__	:	List[Any]				=int(np.ceil((x_end - xa) / step_size			)			)
			lowerCamelCase__	:	Optional[int]				=np.zeros((n + 1,)			)
			lowerCamelCase__	:	List[Any]				=ya
			lowerCamelCase__	:	Any				=xa

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

			return y


if __name__ == "__main__":
		import doctest

		doctest.testmod()









"""simple docstring"""






def   snake_case__     (	__lowerCamelCase       :					int = 4000000			):
			"""simple docstring"""
			lowerCamelCase__	:	Dict				=[]
			lowerCamelCase__			,     lowerCamelCase__	:	Union[str, Any]				=0, 1
			while b <= n:
						if b % 2 == 0:
									even_fibs.append(__lowerCamelCase			)
						lowerCamelCase__			,     lowerCamelCase__	:	Union[str, Any]				=b, a + b
			return sum(__lowerCamelCase			)


if __name__ == "__main__":
		print(f'{solution() = }')




