
'''simple docstring'''


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




def lowercase_	(   _lowercase				)     ->							List[Any]:
					'''simple docstring'''

					def is_in_circle(_lowercase			,       _lowercase				) -> bool:
										lowerCamelCase_					:      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
					lowerCamelCase_					:      Tuple     =		mean(
					    int(is_in_circle(uniform(-1.0			,       1.0				)			,       uniform(-1.0			,       1.0				)				)				)
					    for _ in range(_lowercase				)				)
					# The ratio of the area for circle to square is pi/4.
					lowerCamelCase_					:      Tuple     =		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 lowercase_	(   _lowercase			,       _lowercase			,       _lowercase = 0.0			,       _lowercase = 1.0			,       )     ->							float:
					'''simple docstring'''

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




def lowercase_	(   _lowercase			,       _lowercase = 0.0			,       _lowercase = 1.0				)     ->							None:
					'''simple docstring'''

					def identity_function(_lowercase				) -> float:
										return x

					lowerCamelCase_					:      Tuple     =		area_under_curve_estimator(
					    _lowercase			,       _lowercase			,       _lowercase			,       _lowercase				)
					lowerCamelCase_					:      Optional[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 lowercase_	(   _lowercase				)     ->							None:
					'''simple docstring'''

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

					lowerCamelCase_					:      Union[str, Any]     =		area_under_curve_estimator(
					    _lowercase			,       _lowercase			,       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'''


import os
from math import logaa




def lowercase_	(   _lowercase = "base_exp.txt"				)     ->							int:
					'''simple docstring'''

					lowerCamelCase_					:      float     =		0
					lowerCamelCase_					:      Dict     =		0
					for i, line in enumerate(open(os.path.join(os.path.dirname(_lowercase				)			,       _lowercase				)				)				):
										lowerCamelCase_,      lowerCamelCase_					:      Dict     =		list(map(_lowercase			,       line.split(''','''				)				)				)
										if x * logaa(_lowercase				) > largest:
															lowerCamelCase_					:      List[str]     =		x * logaa(_lowercase				)
															lowerCamelCase_					:      Union[str, Any]     =		i + 1
					return result


if __name__ == "__main__":
					print(solution())


