





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







def  _SCREAMING_SNAKE_CASE				(   a  )      ->      List[Any]:

					# A local function to see if a dot lands in the circle.
					def is_in_circle(a					,						a  ) -> bool:
										__A	:						Any       =				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	:						Dict       =				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[int]       =				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					,						)      ->      float:
					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  )      ->      None:

					def identity_function(a  ) -> float:
										return x

					__A	:						int       =				area_under_curve_estimator(
					    a					,						a					,						a					,						a  )
					__A	:						List[str]       =				(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  )      ->      None:

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

					__A	:						List[Any]       =				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()











from __future__ import annotations







def  _SCREAMING_SNAKE_CASE				(   a  )      ->      int:
					if not nums:
										return 0
					__A	:						Optional[int]       =				nums[0]
					__A	:						str       =				0
					for num in nums[1:]:
										__A    ,				__A	:						Tuple       =				(
										    max_excluding + num,
										    max(a					,						a  ),
										)
					return max(a					,						a  )


if __name__ == "__main__":
				import doctest

				doctest.testmod()




