"""simple docstring"""
import string

# frequency taken from https://en.wikipedia.org/wiki/Letter_frequency
SCREAMING_SNAKE_CASE__      						=  {
    "E": 12.70,
    "T": 9.06,
    "A": 8.17,
    "O": 7.51,
    "I": 6.97,
    "N": 6.75,
    "S": 6.33,
    "H": 6.09,
    "R": 5.99,
    "D": 4.25,
    "L": 4.03,
    "C": 2.78,
    "U": 2.76,
    "M": 2.41,
    "W": 2.36,
    "F": 2.23,
    "G": 2.02,
    "Y": 1.97,
    "P": 1.93,
    "B": 1.29,
    "V": 0.98,
    "K": 0.77,
    "J": 0.15,
    "X": 0.15,
    "Q": 0.10,
    "Z": 0.07,
}
SCREAMING_SNAKE_CASE__      						=  "ETAOINSHRDLCUMWFGYPBVKJXQZ"
SCREAMING_SNAKE_CASE__      						=  "ABCDEFGHIJKLMNOPQRSTUVWXYZ"





def    lowerCAmelCase__    (			_UpperCamelCase       :				str					)					->				dict[str, int]:





						"""simple docstring"""






						snake_case								=			{letter: 0 for letter in string.ascii_uppercase}
						for letter in message.upper():
												if letter in LETTERS:
																		letter_count[letter] += 1

						return letter_count





def    lowerCAmelCase__    (			_UpperCamelCase       :				tuple					)					->				str:





						"""simple docstring"""






						return x[0]





def    lowerCAmelCase__    (			_UpperCamelCase       :				str					)					->				str:





						"""simple docstring"""






						snake_case								=			get_letter_count(_UpperCamelCase					)
						snake_case								=			{
						    freq: [] for letter, freq in letter_to_freq.items()
						}
						for letter in LETTERS:
												freq_to_letter[letter_to_freq[letter]].append(_UpperCamelCase					)

						snake_case								=			{}

						for freq in freq_to_letter:
												freq_to_letter[freq].sort(key=ETAOIN.find ,			reverse=_UpperCamelCase					)
												snake_case								=			''.join(freq_to_letter[freq]					)

						snake_case								=			list(freq_to_letter_str.items()					)
						freq_pairs.sort(key=_UpperCamelCase ,			reverse=_UpperCamelCase					)

						snake_case								=			[freq_pair[1] for freq_pair in freq_pairs]

						return "".join(_UpperCamelCase					)





def    lowerCAmelCase__    (			_UpperCamelCase       :				str					)					->				int:





						"""simple docstring"""






						snake_case								=			get_frequency_order(_UpperCamelCase					)
						snake_case								=			0
						for common_letter in ETAOIN[:6]:
												if common_letter in freq_order[:6]:
																		match_score += 1

						for uncommon_letter in ETAOIN[-6:]:
												if uncommon_letter in freq_order[-6:]:
																		match_score += 1

						return match_score


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()


