
'''simple docstring'''







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







def        SCREAMING_SNAKE_CASE__			(     __A			) ->			Optional[int]:







	def is_in_circle(__A    ,       __A			) -> bool:
		_snake_case     		=	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
	_snake_case     		=	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.
	_snake_case     		=	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        SCREAMING_SNAKE_CASE__			(     __A    ,       __A    ,       __A = 0.0    ,       __A = 1.0    ,       ) ->			Any:
	return mean(
	    function_to_integrate(uniform(__A    ,       __A			)			) for _ in range(__A			)			) * (max_value - min_value)







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A = 0.0    ,       __A = 1.0			) ->			Union[str, Any]:







	def identity_function(__A			) -> float:
		return x

	_snake_case     		=	area_under_curve_estimator(
	    __A    ,       __A    ,       __A    ,       __A			)
	_snake_case     		=	(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        SCREAMING_SNAKE_CASE__			(     __A			) ->			Tuple:







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

	_snake_case     		=	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 abc import ABC, abstractmethod
from argparse import ArgumentParser


class 		__UpperCAmelCase   (      _lowerCamelCase		):


							@staticmethod
							@abstractmethod
							def 				lowerCamelCase       ( lowerCAmelCase_						):





								"""simple docstring"""






								raise NotImplementedError()




							@abstractmethod
							def 				lowerCamelCase       ( self						):





								"""simple docstring"""






								raise NotImplementedError()

