
"""simple docstring"""

from __future__ import annotations

from collections.abc import Callable
def 		UpperCAmelCase					(		a_,						a_,						a_,						a_ = 100,						):





		'''simple docstring'''


		lowerCamelCase     :			List[str]		=    x_start
		lowerCamelCase     :			Union[str, Any]		=    fnc(a_			)
		lowerCamelCase     :			Tuple		=    0.0

		for _ in range(a_			):
				# Approximates small segments of curve as linear and solve
				# for trapezoidal area
				lowerCamelCase     :			List[Any]		=    (x_end - x_start) / steps + xa
				lowerCamelCase     :			Any		=    fnc(a_			)
				area += abs(fxa + fxa			) * (xa - xa) / 2

				# Increment step
				lowerCamelCase     :			Any		=    xa
				lowerCamelCase     :			Union[str, Any]		=    fxa
		return area


if __name__ == "__main__":
					def 		UpperCAmelCase					(		a_			):





							'''simple docstring'''


							return x**3

					print('f(x) = x^3')
					print('The area between the curve, x = -10, x = 10 and the x axis is:')
					_A            = 1_0
					while i <= 1_0_0_0_0_0:
										_A            = trapezoidal_area(f, -5, 5, i)
										print(F"""with {i} steps: {area}""")
										i *= 1_0








"""simple docstring"""

from __future__ import annotations
def 		UpperCAmelCase					(		a_			):





		'''simple docstring'''


		assert (
		    isinstance(a_,						a_			) and mask > 0
		), F"""mask needs to be positive integer, your input {mask}"""
		lowerCamelCase     :			Tuple		=    []
		lowerCamelCase     :			Tuple		=    mask

		while submask:
				all_submasks.append(a_			)
				lowerCamelCase     :			Optional[int]		=    (submask - 1) & mask

		return all_submasks


if __name__ == "__main__":
					import doctest

					doctest.testmod()






