


"""simple docstring"""


import numpy as np


def _lowerCamelCase	(		_UpperCamelCase    , _UpperCamelCase    , _UpperCamelCase    , _UpperCamelCase    , _UpperCamelCase      ):

			'''simple docstring'''




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

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

			return y


if __name__ == "__main__":
	import doctest

	doctest.testmod()







from math import ceil



def    __UpperCAmelCase (	__a      :			int = 1_001	)			->     int:

					"""simple docstring"""

					_a	:    List[Any]         =		1

					for i in range(1		,int(ceil(n / 2.0	)	)	):
										_a	:    Optional[Any]         =		2 * i + 1
										_a	:    Optional[int]         =		2 * i
										_a	:    str         =		total + 4 * odd**2 - 6 * even

					return total


if __name__ == "__main__":
			import sys

			if len(sys.argv) == 1:
						print(solution())
			else:
						try:
									a__				=		int(sys.argv[1])
									print(solution(n))
						except ValueError:
									print('''Invalid entry - please enter a number''')



