




'''simple docstring'''





from __future__ import annotations

from collections.abc import Callable

def 			lowerCAmelCase_			(  lowerCamelCase:       Tuple     ,				lowerCamelCase:       Optional[int]     ,				lowerCamelCase:       Optional[int]     ,				lowerCamelCase:       List[str] = 1_00     ,				)					->			float:


      '''simple docstring'''




      lowerCamelCase__        =				x_start
      lowerCamelCase__        =				fnc(_UpperCAmelCase						)
      lowerCamelCase__        =				0.0

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

            # Increment step
            lowerCamelCase__        =				xa
            lowerCamelCase__        =				fxa
      return area


if __name__ == "__main__":

      def 			lowerCAmelCase_			(  lowerCamelCase:       int						)					->			Optional[int]:


            '''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:""")
      __SCREAMING_SNAKE_CASE    :   Tuple       =10
      while i <= 100_000:
            __SCREAMING_SNAKE_CASE    :   Optional[int]       =trapezoidal_area(f, -5, 5, i)
            print(F"""with {i} steps: {area}""")
            i *= 10





from ..utils import DummyObject, requires_backends






class 			A			(		metaclass=_lowerCAmelCase		):
     """simple docstring"""

     _snake_case:	Optional[Any]     =["torch", "transformers", "invisible_watermark"]




     def __init__(    self  :   Dict	,  *A__  :   Optional[int]	,  **A__  :   Dict			)				->       Union[str, Any]:
           requires_backends(self	,  ['torch', 'transformers', 'invisible_watermark']			)




     @classmethod
     def  __snake_case   (    cls  :   Optional[int]	,  *A__  :   Dict	,  **A__  :   List[str]			)				->       Union[str, Any]:
           requires_backends(cls	,  ['torch', 'transformers', 'invisible_watermark']			)




     @classmethod
     def  __snake_case   (    cls  :   Optional[Any]	,  *A__  :   Dict	,  **A__  :   List[Any]			)				->       Dict:
           requires_backends(cls	,  ['torch', 'transformers', 'invisible_watermark']			)






class 			A			(		metaclass=_lowerCAmelCase		):
     """simple docstring"""

     _snake_case:	Dict     =["torch", "transformers", "invisible_watermark"]




     def __init__(    self  :   List[str]	,  *A__  :   str	,  **A__  :   int			)				->       List[Any]:
           requires_backends(self	,  ['torch', 'transformers', 'invisible_watermark']			)




     @classmethod
     def  __snake_case   (    cls  :   str	,  *A__  :   Any	,  **A__  :   Dict			)				->       Optional[Any]:
           requires_backends(cls	,  ['torch', 'transformers', 'invisible_watermark']			)




     @classmethod
     def  __snake_case   (    cls  :   List[str]	,  *A__  :   Optional[Any]	,  **A__  :   int			)				->       Dict:
           requires_backends(cls	,  ['torch', 'transformers', 'invisible_watermark']			)