





from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean



def A_	(		A__				)  ->		Tuple:

       # A local function to see if a dot lands in the circle.
       def is_in_circle(A__		,      A__				) -> bool:
              a__						:	List[str] =				sqrt((x**2) + (y**2)				)
              # Our circle has a radius of 1, so a distance
              # greater than 1 would land outside the circle.
              return distance_from_centre <= 1

       # The proportion of guesses that landed in the circle
       a__						:	List[str] =				mean(
           int(is_in_circle(uniform(-1.0		,      1.0				)		,      uniform(-1.0		,      1.0				)				)				)
           for _ in range(A__				)				)
       # The ratio of the area for circle to square is pi/4.
       a__						:	Optional[Any] =				proportion * 4
       print(F'The estimated value of pi is {pi_estimate}'				)
       print(F'The numpy value of pi is {pi}'				)
       print(F'The total error is {abs(pi - pi_estimate				)}'				)



def A_	(		A__		,      A__		,      A__ = 0.0		,      A__ = 1.0		,      )  ->		float:
       return mean(
           function_to_integrate(uniform(A__		,      A__				)				) for _ in range(A__				)				) * (max_value - min_value)



def A_	(		A__		,      A__ = 0.0		,      A__ = 1.0				)  ->		None:

       def identity_function(A__				) -> float:
              return x

       a__						:	List[Any] =				area_under_curve_estimator(
           A__		,      A__		,      A__		,      A__				)
       a__						:	Union[str, Any] =				(max_value * max_value - min_value * min_value) / 2

       print('******************'				)
       print(F'Estimating area under y=x where x varies from {min_value} to {max_value}'				)
       print(F'Estimated value is {estimated_value}'				)
       print(F'Expected value is {expected_value}'				)
       print(F'Total error is {abs(estimated_value - expected_value				)}'				)
       print('******************'				)



def A_	(		A__				)  ->		None:

       def function_to_integrate(A__				) -> float:
              return sqrt(4.0 - x * x				)

       a__						:	Dict =				area_under_curve_estimator(
           A__		,      A__		,      0.0		,      2.0				)

       print('******************'				)
       print('Estimating pi using area_under_curve_estimator'				)
       print(F'Estimated value is {estimated_value}'				)
       print(F'Expected value is {pi}'				)
       print(F'Total error is {abs(estimated_value - pi				)}'				)
       print('******************'				)


if __name__ == "__main__":
    import doctest

    doctest.testmod()



"""simple docstring"""






from ..utils import DummyObject, requires_backends





class  _A						(       metaclass=lowerCAmelCase	):
      snake_case__			:   str							  =	['torch', 'transformers', 'onnx']

      def __init__(						self		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(self		,       ["""torch""", """transformers""", """onnx"""]						)

      @classmethod
      def 				A__       (						cls		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(cls		,       ["""torch""", """transformers""", """onnx"""]						)







      @classmethod
      def 				A__       (						cls		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(cls		,       ["""torch""", """transformers""", """onnx"""]						)






class  _A						(       metaclass=lowerCAmelCase	):
      snake_case__			:   List[Any]							  =	['torch', 'transformers', 'onnx']

      def __init__(						self		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(self		,       ["""torch""", """transformers""", """onnx"""]						)

      @classmethod
      def 				A__       (						cls		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(cls		,       ["""torch""", """transformers""", """onnx"""]						)







      @classmethod
      def 				A__       (						cls		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(cls		,       ["""torch""", """transformers""", """onnx"""]						)






class  _A						(       metaclass=lowerCAmelCase	):
      snake_case__			:   Optional[Any]							  =	['torch', 'transformers', 'onnx']

      def __init__(						self		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(self		,       ["""torch""", """transformers""", """onnx"""]						)

      @classmethod
      def 				A__       (						cls		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(cls		,       ["""torch""", """transformers""", """onnx"""]						)







      @classmethod
      def 				A__       (						cls		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(cls		,       ["""torch""", """transformers""", """onnx"""]						)






class  _A						(       metaclass=lowerCAmelCase	):
      snake_case__			:   int							  =	['torch', 'transformers', 'onnx']

      def __init__(						self		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(self		,       ["""torch""", """transformers""", """onnx"""]						)

      @classmethod
      def 				A__       (						cls		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(cls		,       ["""torch""", """transformers""", """onnx"""]						)







      @classmethod
      def 				A__       (						cls		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(cls		,       ["""torch""", """transformers""", """onnx"""]						)






class  _A						(       metaclass=lowerCAmelCase	):
      snake_case__			:   List[str]							  =	['torch', 'transformers', 'onnx']

      def __init__(						self		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(self		,       ["""torch""", """transformers""", """onnx"""]						)

      @classmethod
      def 				A__       (						cls		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(cls		,       ["""torch""", """transformers""", """onnx"""]						)







      @classmethod
      def 				A__       (						cls		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(cls		,       ["""torch""", """transformers""", """onnx"""]						)






class  _A						(       metaclass=lowerCAmelCase	):
      snake_case__			:   Optional[Any]							  =	['torch', 'transformers', 'onnx']

      def __init__(						self		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(self		,       ["""torch""", """transformers""", """onnx"""]						)

      @classmethod
      def 				A__       (						cls		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(cls		,       ["""torch""", """transformers""", """onnx"""]						)







      @classmethod
      def 				A__       (						cls		,       *__lowerCAmelCase		,       **__lowerCAmelCase						):







            """simple docstring"""



            requires_backends(cls		,       ["""torch""", """transformers""", """onnx"""]						)



