



from __future__ import annotations

from collections.abc import Callable

def    lowerCamelCase_(lowerCamelCase_    ,   lowerCamelCase_    ,   lowerCamelCase_    ,   lowerCamelCase_ = 100    ,   ) ->       List[str]:
						UpperCAmelCase         =     x_start
						UpperCAmelCase         =     fnc(__snake_case    )
						UpperCAmelCase         =     0.0
						for _ in range(__snake_case    ):
												# Approximates small segments of curve as linear and solve
												# for trapezoidal area
												UpperCAmelCase         =     (x_end - x_start) / steps + xa
												UpperCAmelCase         =     fnc(__snake_case    )
												area += abs(fxa + fxa    ) * (xa - xa) / 2
												# Increment step
												UpperCAmelCase         =     xa
												UpperCAmelCase         =     fxa
						return area


if __name__ == "__main__":

		def    lowerCamelCase_(lowerCamelCase_    ) ->       List[str]:
								return x**3 + x**2

		print("f(x) = x^3 + x^2")
		print("The area between the curve, x = -5, x = 5 and the x axis is:")
		__lowerCamelCase     :							Union[str, Any]  							=  10
		while i <= 100_000:
				print(F'''with {i} steps: {trapezoidal_area(f, -5, 5, i)}''')
				i *= 10








from ..utils import DummyObject, requires_backends





class  __magic_name__   (							metaclass=A__						):
		lowercase      :       int          =['''note_seq''']






		def __init__(						self      :     List[Any]				,		*UpperCamelCase__      :     Tuple				,		**UpperCamelCase__      :     Dict      )				->					int:
								'''simple docstring'''







								requires_backends(self				,		["note_seq"]      )






		@classmethod
		def SCREAMING_SNAKE_CASE_			(						cls      :     List[str]				,		*UpperCamelCase__      :     Dict				,		**UpperCamelCase__      :     str      )				->					Optional[int]:
								'''simple docstring'''







								requires_backends(cls				,		["note_seq"]      )







		@classmethod
		def SCREAMING_SNAKE_CASE_			(						cls      :     List[Any]				,		*UpperCamelCase__      :     Optional[int]				,		**UpperCamelCase__      :     Optional[Any]      )				->					Optional[int]:
								'''simple docstring'''







								requires_backends(cls				,		["note_seq"]      )



