





import numpy as np




def    A_(			A				,      A				,      A				,      A				,      A   ):
	UpperCAmelCase_								=     int(np.ceil((x_end - xa) / h   )   )
	UpperCAmelCase_								=     np.zeros((n + 1,)   )
	UpperCAmelCase_								=     ya
	UpperCAmelCase_								=     xa

	for k in range(A   ):
		UpperCAmelCase_								=     f(A				,      y[k]   )
		UpperCAmelCase_								=     f(x + 0.5 * h				,      y[k] + 0.5 * h * ka   )
		UpperCAmelCase_								=     f(x + 0.5 * h				,      y[k] + 0.5 * h * ka   )
		UpperCAmelCase_								=     f(x + h				,      y[k] + h * ka   )
		UpperCAmelCase_								=     y[k] + (1 / 6) * h * (ka + 2 * ka + 2 * ka + ka)
		x += h

	return y


if __name__ == "__main__":
				import doctest

				doctest.testmod()









from __future__ import annotations




def    A_(			A   ):
	if not nums:
		raise ValueError("""List is empty"""   )
	return sum(A   ) / len(A   )


if __name__ == "__main__":
				import doctest

				doctest.testmod()


