

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



def      __lowerCAmelCase			(					UpperCamelCase      )     ->	int:

  # A local function to see if a dot lands in the circle.
  def is_in_circle(UpperCamelCase	,      UpperCamelCase      ) -> bool:
    lowerCAmelCase__				:  Optional[int]		       =     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
  lowerCAmelCase__				:  Optional[int]		       =     mean(
      int(is_in_circle(uniform(-1.0	,      1.0      )	,      uniform(-1.0	,      1.0      )      )      )
      for _ in range(UpperCamelCase      )      )
  # The ratio of the area for circle to square is pi/4.
  lowerCAmelCase__				:  Union[str, 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      __lowerCAmelCase			(					UpperCamelCase	,      UpperCamelCase	,      UpperCamelCase = 0.0	,      UpperCamelCase = 1.0	,      )     ->	float:
  return mean(
      function_to_integrate(uniform(UpperCamelCase	,      UpperCamelCase      )      ) for _ in range(UpperCamelCase      )      ) * (max_value - min_value)



def      __lowerCAmelCase			(					UpperCamelCase	,      UpperCamelCase = 0.0	,      UpperCamelCase = 1.0      )     ->	None:

  def identity_function(UpperCamelCase      ) -> float:
    return x

  lowerCAmelCase__				:  int		       =     area_under_curve_estimator(
      UpperCamelCase	,      UpperCamelCase	,      UpperCamelCase	,      UpperCamelCase      )
  lowerCAmelCase__				:  List[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      __lowerCAmelCase			(					UpperCamelCase      )     ->	None:

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

  lowerCAmelCase__				:  Optional[int]		       =     area_under_curve_estimator(
      UpperCamelCase	,      UpperCamelCase	,      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()







import warnings

from diffusers import StableDiffusionInpaintPipeline as StableDiffusionInpaintPipeline  # noqa F401


warnings.warn(
    """The `inpainting.py` script is outdated. Please use directly `from diffusers import"""
    """ StableDiffusionInpaintPipeline` instead."""
)

