

'''simple docstring'''







from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean
def       UpperCAmelCase__    (      UpperCAmelCase__				)			->			Dict:

       # A local function to see if a dot lands in the circle.
       def is_in_circle(UpperCAmelCase__,       UpperCAmelCase__				) -> bool:
              A_						=      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
       A_						=      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.
       A_						=      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       UpperCAmelCase__    (      UpperCAmelCase__,       UpperCAmelCase__,       UpperCAmelCase__ = 0.0,       UpperCAmelCase__ = 1.0,       )			->			Any:
       return mean(
           function_to_integrate(uniform(lowercase__,       lowercase__				)				) for _ in range(lowercase__				)				) * (max_value - min_value)
def       UpperCAmelCase__    (      UpperCAmelCase__,       UpperCAmelCase__ = 0.0,       UpperCAmelCase__ = 1.0				)			->			Any:

       def identity_function(UpperCAmelCase__				) -> float:
              return x

       A_						=      area_under_curve_estimator(
           lowercase__,       lowercase__,       lowercase__,       lowercase__				)
       A_						=      (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       UpperCAmelCase__    (      UpperCAmelCase__				)			->			int:

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

       A_						=      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

__lowerCamelCase		       =    {'''I''': 1, '''V''': 5, '''X''': 10, '''L''': 50, '''C''': 100, '''D''': 500, '''M''': 1000}
def       UpperCAmelCase__    (      UpperCAmelCase__				)			->			int:
       A_						=      0

       A_						=      0
       while index < len(UpperCAmelCase__				) - 1:
              A_						=      SYMBOLS[numerals[index]]
              A_						=      SYMBOLS[numerals[index + 1]]
              if current_value < next_value:
                     total_value -= current_value
              else:
                     total_value += current_value
              index += 1
       total_value += SYMBOLS[numerals[index]]

       return total_value
def       UpperCAmelCase__    (      UpperCAmelCase__				)			->			str:
       A_						=      """"""

       A_						=      num // 10_00
       numerals += m_count * "M"
       num %= 10_00

       A_						=      num // 1_00
       if c_count == 9:
              numerals += "CM"
              c_count -= 9
       elif c_count == 4:
              numerals += "CD"
              c_count -= 4
       if c_count >= 5:
              numerals += "D"
              c_count -= 5
       numerals += c_count * "C"
       num %= 1_00

       A_						=      num // 10
       if x_count == 9:
              numerals += "XC"
              x_count -= 9
       elif x_count == 4:
              numerals += "XL"
              x_count -= 4
       if x_count >= 5:
              numerals += "L"
              x_count -= 5
       numerals += x_count * "X"
       num %= 10

       if num == 9:
              numerals += "IX"
              num -= 9
       elif num == 4:
              numerals += "IV"
              num -= 4
       if num >= 5:
              numerals += "V"
              num -= 5
       numerals += num * "I"

       return numerals
def       UpperCAmelCase__    (      UpperCAmelCase__ = "/p089_roman.txt"				)			->			int:
       A_						=      0

       with open(os.path.dirname(UpperCAmelCase__				) + roman_numerals_filename				) as filea:
              A_						=      filea.readlines()

       for line in lines:
              A_						=      line.strip()
              A_						=      parse_roman_numerals(UpperCAmelCase__				)
              A_						=      generate_roman_numerals(UpperCAmelCase__				)
              savings += len(UpperCAmelCase__				) - len(UpperCAmelCase__				)

       return savings


if __name__ == "__main__":
      print(f"""{solution() = }""")
