from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean
def 					_snake_case	(  __snake_case						):

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

					def identity_function(__snake_case						) -> float:
										return x

					_UpperCamelCase			     =     area_under_curve_estimator(
					    __snake_case  ,     __snake_case  ,     __snake_case  ,     __snake_case						)
					_UpperCamelCase			     =     (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 					_snake_case	(  __snake_case						):

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

					_UpperCamelCase			     =     area_under_curve_estimator(
					    __snake_case  ,     __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()




SCREAMING_SNAKE_CASE__					:     dict[str, float]       =     {
    "joule": 1.0,
    "kilojoule": 1_000,
    "megajoule": 1_000_000,
    "gigajoule": 1_000_000_000,
    "wattsecond": 1.0,
    "watthour": 3_600,
    "kilowatthour": 3_600_000,
    "newtonmeter": 1.0,
    "calorie_nutr": 4_186.8,
    "kilocalorie_nutr": 4_186_800.00,
    "electronvolt": 1.602176634e-19,
    "britishthermalunit_it": 1_055.05_585,
    "footpound": 1.355_818,
}




def    a__    (		snake_case__					:							str						,   snake_case__					:							str						,   snake_case__					:							float     ):
  if to_type not in ENERGY_CONVERSION or from_type not in ENERGY_CONVERSION:
    _UpperCAmelCase		:							Optional[Any]							=     (
        f'''Incorrect \'from_type\' or \'to_type\' value: {from_type!r}, {to_type!r}\n'''
        f'''Valid values are: {", ".join(snake_case__     )}'''
    )
    raise ValueError(snake_case__     )
  return value * ENERGY_CONVERSION[from_type] / ENERGY_CONVERSION[to_type]


if __name__ == "__main__":
 import doctest

 doctest.testmod()





