


from __future__ import annotations


def 				lowerCamelCase__	(      a	:   list[int]	,  a	:   list[int]	,  a	:   int				)    ->	tuple[float, list[float]]:





			"""simple docstring"""
			a__ :Dict						  =    list(range(len(a				)				)				)
			a__ :List[Any]						  =    [v / w for v, w in zip(a	,  a				)]
			index.sort(key=lambda a				: ratio[i]	,  reverse=a				)

			a__ :float						  =    0
			a__ :list[float]						  =    [0] * len(a				)
			for i in index:
						if weight[i] <= capacity:
									a__ :Optional[Any]						  =    1
									max_value += value[i]
									capacity -= weight[i]
						else:
									a__ :Union[str, Any]						  =    capacity / weight[i]
									max_value += value[i] * capacity / weight[i]
									break

			return max_value, fractions


if __name__ == "__main__":
		import doctest

		doctest.testmod()






def 				lowerCamelCase__	(      a	:   int	,  a	:   int				)    ->	Any:





			"""simple docstring"""
			# "extended trapezoidal rule"
			# int(f) = dx/2 * (f1 + 2f2 + ... + fn)
			a__ :Optional[int]						  =    (boundary[1] - boundary[0]) / steps
			a__ :str						  =    boundary[0]
			a__ :Optional[int]						  =    boundary[1]
			a__ :str						  =    make_points(a	,  a	,  a				)
			a__ :Any						  =    0.0
			y += (h / 2.0) * f(a				)
			for i in x_i:
						# print(i)
						y += h * f(a				)
			y += (h / 2.0) * f(a				)
			return y


def 				lowerCamelCase__	(      a	:   Any	,  a	:   str	,  a	:   Dict				)    ->	int:





			"""simple docstring"""
			a__ :Union[str, Any]						  =    a + h
			while x < (b - h):
						yield x
						a__ :str						  =    x + h


def 				lowerCamelCase__	(      a	:   Optional[int]				)    ->	List[Any]:  # enter your function here





			"""simple docstring"""
			a__ :Tuple						  =    (x - 0) * (x - 0)
			return y


def 				lowerCamelCase__	(      )    ->	List[str]:





			"""simple docstring"""
			a__ :Optional[Any]						  =    0.0  # Lower bound of integration
			a__ :Optional[Any]						  =    1.0  # Upper bound of integration
			a__ :List[str]						  =    1_0.0  # define number of steps or resolution
			a__ :int						  =    [a, b]  # define boundary of integration
			a__ :str						  =    method_a(a	,  a				)
			print(F'''y = {y}'''				)


if __name__ == "__main__":
		main()


