






def 		lowercase__  (				_UpperCamelCase) ->			List[Any]:
      """simple docstring"""

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

      UpperCamelCase					       =  hex_num[0] == "-"
      if is_negative:
            UpperCamelCase					       =  hex_num[1:]

      try:
            UpperCamelCase					       =  int(_UpperCamelCase       ,							16)
      except ValueError:
            raise ValueError('Invalid value was passed to the function')

      UpperCamelCase					       =  ""
      while int_num > 0:
            UpperCamelCase					       =  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()






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



def 			_A	(      SCREAMING_SNAKE_CASE      ):

	# A local function to see if a dot lands in the circle.
	def is_in_circle(SCREAMING_SNAKE_CASE	,SCREAMING_SNAKE_CASE      ) -> bool:
		UpperCAmelCase__:	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
	UpperCAmelCase__:	Optional[int]									= mean(
	    int(is_in_circle(uniform(-1.0	,1.0      )	,uniform(-1.0	,1.0      )      )      )
	    for _ in range(SCREAMING_SNAKE_CASE      )      )
	# The ratio of the area for circle to square is pi/4.
	UpperCAmelCase__:	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 			_A	(      SCREAMING_SNAKE_CASE	,SCREAMING_SNAKE_CASE	,SCREAMING_SNAKE_CASE = 0.0	,SCREAMING_SNAKE_CASE = 1.0	,):
	return mean(
	    function_to_integrate(uniform(SCREAMING_SNAKE_CASE	,SCREAMING_SNAKE_CASE      )      ) for _ in range(SCREAMING_SNAKE_CASE      )      ) * (max_value - min_value)



def 			_A	(      SCREAMING_SNAKE_CASE	,SCREAMING_SNAKE_CASE = 0.0	,SCREAMING_SNAKE_CASE = 1.0      ):

	def identity_function(SCREAMING_SNAKE_CASE      ) -> float:
		return x

	UpperCAmelCase__:	Tuple									= area_under_curve_estimator(
	    SCREAMING_SNAKE_CASE	,SCREAMING_SNAKE_CASE	,SCREAMING_SNAKE_CASE	,SCREAMING_SNAKE_CASE      )
	UpperCAmelCase__:	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 			_A	(      SCREAMING_SNAKE_CASE      ):

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

	UpperCAmelCase__:	Union[str, Any]									= area_under_curve_estimator(
	    SCREAMING_SNAKE_CASE	,SCREAMING_SNAKE_CASE	,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()