"""simple docstring"""
def    lowerCAmelCase__    (			_UpperCamelCase       :				str					)					->				int:





						"""simple docstring"""






						snake_case								=			hex_num.strip()
						if not hex_num:
												raise ValueError('No value was passed to the function'					)

						snake_case								=			hex_num[0] == '-'
						if is_negative:
												snake_case								=			hex_num[1:]

						try:
												snake_case								=			int(_UpperCamelCase ,			1_6					)
						except ValueError:
												raise ValueError('Invalid value was passed to the function'					)

						snake_case								=			''
						while int_num > 0:
												snake_case								=			str(int_num % 2					) + bin_str
												int_num >>= 1

						return int(('-' + bin_str) if is_negative else bin_str					)


if __name__ == "__main__":
					import doctest

					doctest.testmod()



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





def    lowerCAmelCase__    (			_UpperCamelCase       :				int					)					->				Dict:





						"""simple docstring"""






						def is_in_circle(_UpperCamelCase       :				float ,			_UpperCamelCase       :				float					) -> 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(_UpperCamelCase					)					)
						# 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    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

						snake_case								=			area_under_curve_estimator(
						    _UpperCamelCase ,			_UpperCamelCase ,			_UpperCamelCase ,			_UpperCamelCase					)
						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    lowerCAmelCase__    (			_UpperCamelCase       :				int					)					->				None:





						"""simple docstring"""






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

						snake_case								=			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()


