




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







def 			lowerCamelCase_		(       UpperCamelCase__				:      int      )     ->       List[str]:





				"""simple docstring"""


				def is_in_circle(UpperCamelCase__				:      float ,     UpperCamelCase__				:      float      ) -> bool:
								__lowerCamelCase		       =    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		       =    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		       =    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__				:      int ,     UpperCamelCase__				:      Callable[[float], float] ,     UpperCamelCase__				:      float = 0.0 ,     UpperCamelCase__				:      float = 1.0 ,     )     ->       float:





				"""simple docstring"""


				return mean(
				    function_to_integrate(uniform(UpperCamelCase__ ,     UpperCamelCase__      )      ) for _ in range(UpperCamelCase__      )      ) * (max_value - min_value)







def 			lowerCamelCase_		(       UpperCamelCase__				:      int ,     UpperCamelCase__				:      float = 0.0 ,     UpperCamelCase__				:      float = 1.0      )     ->       None:





				"""simple docstring"""


				def identity_function(UpperCamelCase__				:      float      ) -> float:
								return x

				__lowerCamelCase		       =    area_under_curve_estimator(
				    UpperCamelCase__ ,     UpperCamelCase__ ,     UpperCamelCase__ ,     UpperCamelCase__      )
				__lowerCamelCase		       =    (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__				:      int      )     ->       None:





				"""simple docstring"""


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

				__lowerCamelCase		       =    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 ...utils import logging
from .image_processing_donut import DonutImageProcessor


A_       : Union[str, Any]         =			logging.get_logger(__name__)



class     _a						(__magic_name__				):


					'''simple docstring'''






					def __init__( self    ,       *A__    ,       **A__			):
						warnings.warn(
						    """The class DonutFeatureExtractor is deprecated and will be removed in version 5 of Transformers. Please"""
						    """ use DonutImageProcessor instead."""    ,       A__    ,       )
						super().__init__(*A__    ,       **A__			)



