


"""simple docstring"""
from __future__ import annotations

from collections.abc import Callable

def 				_snake_case      (   __snake_case							:      Callable[[int | float], int | float]						, __snake_case							:      int | float						, __snake_case							:      int | float						, __snake_case							:      int = 100						, ):




   """simple docstring"""







   _lowerCamelCase	:					Optional[int]   =		x_start
   _lowerCamelCase	:					Optional[int]   =		fnc(__snake_case   )
   _lowerCamelCase	:					Optional[int]   =		0.0
   for _ in range(__snake_case   ):
      # Approximates small segments of curve as linear and solve
      # for trapezoidal area
      _lowerCamelCase	:					int   =		(x_end - x_start) / steps + xa
      _lowerCamelCase	:					List[Any]   =		fnc(__snake_case   )
      area += abs(fxa + fxa   ) * (xa - xa) / 2
      # Increment step
      _lowerCamelCase	:					List[Any]   =		xa
      _lowerCamelCase	:					Any   =		fxa
   return area


if __name__ == "__main__":

 def 				_snake_case      (   __snake_case							:      List[Any]   ):




    """simple docstring"""







    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:""")
 UpperCAmelCase				=						10
 while i <= 10_0000:
  print(f'''with {i} steps: {trapezoidal_area(f, -5, 5, i)}''')
  i *= 10








'''simple docstring'''




from ..utils import DummyObject, requires_backends




class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			Optional[int]      ,						*lowerCamelCase_				:			Any      ,						**lowerCamelCase_				:			Dict						):

							'''simple docstring'''



							requires_backends(self      ,						["""flax"""]						)


					@classmethod
					def lowerCamelCase_			(						cls				:			Optional[int]      ,						*lowerCamelCase_				:			List[Any]      ,						**lowerCamelCase_				:			str						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)



					@classmethod
					def lowerCamelCase_			(						cls				:			int      ,						*lowerCamelCase_				:			Union[str, Any]      ,						**lowerCamelCase_				:			int						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			List[str]      ,						*lowerCamelCase_				:			Union[str, Any]      ,						**lowerCamelCase_				:			str						):

							'''simple docstring'''



							requires_backends(self      ,						["""flax"""]						)


					@classmethod
					def lowerCamelCase_			(						cls				:			Dict      ,						*lowerCamelCase_				:			Optional[Any]      ,						**lowerCamelCase_				:			Union[str, Any]						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)



					@classmethod
					def lowerCamelCase_			(						cls				:			List[Any]      ,						*lowerCamelCase_				:			Dict      ,						**lowerCamelCase_				:			Dict						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			Optional[Any]      ,						*lowerCamelCase_				:			Optional[int]      ,						**lowerCamelCase_				:			Union[str, Any]						):

							'''simple docstring'''



							requires_backends(self      ,						["""flax"""]						)


					@classmethod
					def lowerCamelCase_			(						cls				:			str      ,						*lowerCamelCase_				:			int      ,						**lowerCamelCase_				:			Dict						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)



					@classmethod
					def lowerCamelCase_			(						cls				:			Optional[Any]      ,						*lowerCamelCase_				:			str      ,						**lowerCamelCase_				:			List[Any]						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			List[Any]      ,						*lowerCamelCase_				:			Tuple      ,						**lowerCamelCase_				:			int						):

							'''simple docstring'''



							requires_backends(self      ,						["""flax"""]						)


					@classmethod
					def lowerCamelCase_			(						cls				:			int      ,						*lowerCamelCase_				:			Dict      ,						**lowerCamelCase_				:			Tuple						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)



					@classmethod
					def lowerCamelCase_			(						cls				:			Any      ,						*lowerCamelCase_				:			str      ,						**lowerCamelCase_				:			Optional[Any]						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			List[str]      ,						*lowerCamelCase_				:			Dict      ,						**lowerCamelCase_				:			int						):

							'''simple docstring'''



							requires_backends(self      ,						["""flax"""]						)


					@classmethod
					def lowerCamelCase_			(						cls				:			Any      ,						*lowerCamelCase_				:			Any      ,						**lowerCamelCase_				:			Any						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)



					@classmethod
					def lowerCamelCase_			(						cls				:			Any      ,						*lowerCamelCase_				:			Optional[int]      ,						**lowerCamelCase_				:			str						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			Any      ,						*lowerCamelCase_				:			List[Any]      ,						**lowerCamelCase_				:			Any						):

							'''simple docstring'''



							requires_backends(self      ,						["""flax"""]						)


					@classmethod
					def lowerCamelCase_			(						cls				:			Union[str, Any]      ,						*lowerCamelCase_				:			Union[str, Any]      ,						**lowerCamelCase_				:			Union[str, Any]						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)



					@classmethod
					def lowerCamelCase_			(						cls				:			List[Any]      ,						*lowerCamelCase_				:			str      ,						**lowerCamelCase_				:			Optional[int]						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			Dict      ,						*lowerCamelCase_				:			Optional[Any]      ,						**lowerCamelCase_				:			int						):

							'''simple docstring'''



							requires_backends(self      ,						["""flax"""]						)


					@classmethod
					def lowerCamelCase_			(						cls				:			int      ,						*lowerCamelCase_				:			Tuple      ,						**lowerCamelCase_				:			Dict						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)



					@classmethod
					def lowerCamelCase_			(						cls				:			Tuple      ,						*lowerCamelCase_				:			int      ,						**lowerCamelCase_				:			Union[str, Any]						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			Optional[Any]      ,						*lowerCamelCase_				:			Dict      ,						**lowerCamelCase_				:			List[Any]						):

							'''simple docstring'''



							requires_backends(self      ,						["""flax"""]						)


					@classmethod
					def lowerCamelCase_			(						cls				:			List[Any]      ,						*lowerCamelCase_				:			Optional[Any]      ,						**lowerCamelCase_				:			List[str]						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)



					@classmethod
					def lowerCamelCase_			(						cls				:			List[str]      ,						*lowerCamelCase_				:			Tuple      ,						**lowerCamelCase_				:			Tuple						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			Dict      ,						*lowerCamelCase_				:			int      ,						**lowerCamelCase_				:			Any						):

							'''simple docstring'''



							requires_backends(self      ,						["""flax"""]						)


					@classmethod
					def lowerCamelCase_			(						cls				:			int      ,						*lowerCamelCase_				:			int      ,						**lowerCamelCase_				:			Any						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)



					@classmethod
					def lowerCamelCase_			(						cls				:			List[Any]      ,						*lowerCamelCase_				:			Tuple      ,						**lowerCamelCase_				:			Tuple						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			int      ,						*lowerCamelCase_				:			Tuple      ,						**lowerCamelCase_				:			Any						):

							'''simple docstring'''



							requires_backends(self      ,						["""flax"""]						)


					@classmethod
					def lowerCamelCase_			(						cls				:			List[Any]      ,						*lowerCamelCase_				:			Tuple      ,						**lowerCamelCase_				:			Optional[Any]						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)



					@classmethod
					def lowerCamelCase_			(						cls				:			List[Any]      ,						*lowerCamelCase_				:			Optional[int]      ,						**lowerCamelCase_				:			Any						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			List[Any]      ,						*lowerCamelCase_				:			List[Any]      ,						**lowerCamelCase_				:			List[Any]						):

							'''simple docstring'''



							requires_backends(self      ,						["""flax"""]						)


					@classmethod
					def lowerCamelCase_			(						cls				:			List[Any]      ,						*lowerCamelCase_				:			Optional[Any]      ,						**lowerCamelCase_				:			Optional[int]						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)



					@classmethod
					def lowerCamelCase_			(						cls				:			Any      ,						*lowerCamelCase_				:			Dict      ,						**lowerCamelCase_				:			Optional[int]						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			Any      ,						*lowerCamelCase_				:			Dict      ,						**lowerCamelCase_				:			int						):

							'''simple docstring'''



							requires_backends(self      ,						["""flax"""]						)


					@classmethod
					def lowerCamelCase_			(						cls				:			List[Any]      ,						*lowerCamelCase_				:			Union[str, Any]      ,						**lowerCamelCase_				:			List[str]						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)



					@classmethod
					def lowerCamelCase_			(						cls				:			Optional[Any]      ,						*lowerCamelCase_				:			Dict      ,						**lowerCamelCase_				:			Optional[Any]						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)







class      UpperCamelCase__					(					metaclass=lowercase_			):




					"""simple docstring"""
					SCREAMING_SNAKE_CASE__				=	['''flax''']


					def __init__(						self				:			Tuple      ,						*lowerCamelCase_				:			Tuple      ,						**lowerCamelCase_				:			Union[str, Any]						):

							'''simple docstring'''



							requires_backends(self      ,						["""flax"""]						)


					@classmethod
					def lowerCamelCase_			(						cls				:			Optional[Any]      ,						*lowerCamelCase_				:			Any      ,						**lowerCamelCase_				:			Optional[int]						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)



					@classmethod
					def lowerCamelCase_			(						cls				:			List[Any]      ,						*lowerCamelCase_				:			Any      ,						**lowerCamelCase_				:			Tuple						):

							'''simple docstring'''



							requires_backends(cls      ,						["""flax"""]						)



