


"""simple docstring"""







from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean
def  a__      (    SCREAMING_SNAKE_CASE   :   int    ):


  '''simple docstring'''







  def is_in_circle(SCREAMING_SNAKE_CASE   :   float    ,				SCREAMING_SNAKE_CASE   :   float    ) -> bool:
    lowerCAmelCase					:					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
  lowerCAmelCase					:					Any								=							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.
  lowerCAmelCase					:					List[str]								=							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   :   int    ,				SCREAMING_SNAKE_CASE   :   Callable[[float], float]    ,				SCREAMING_SNAKE_CASE   :   float = 0.0    ,				SCREAMING_SNAKE_CASE   :   float = 1.0    ,				):


  '''simple docstring'''







  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   :   int    ,				SCREAMING_SNAKE_CASE   :   float = 0.0    ,				SCREAMING_SNAKE_CASE   :   float = 1.0    ):


  '''simple docstring'''







  def identity_function(SCREAMING_SNAKE_CASE   :   float    ) -> float:
    return x

  lowerCAmelCase					:					Union[str, Any]								=							area_under_curve_estimator(
      SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE    )
  lowerCAmelCase					:					Optional[int]								=							(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   :   int    ):


  '''simple docstring'''







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

  lowerCAmelCase					:					Dict								=							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()









"""simple docstring"""







import re

from filelock import FileLock


try:
     import nltk

     lowerCAmelCase__				    =       True
except (ImportError, ModuleNotFoundError):
     lowerCAmelCase__				    =       False

if NLTK_AVAILABLE:
     with FileLock('''.lock''') as lock:
          nltk.download('''punkt''', quiet=True)
def  a__      (    SCREAMING_SNAKE_CASE   :   str    ):


  '''simple docstring'''







  re.sub("<n>"    ,				""    ,				SCREAMING_SNAKE_CASE    )  # remove pegasus newline char
  assert NLTK_AVAILABLE, "nltk must be installed to separate newlines between sentences. (pip install nltk)"
  return "\n".join(nltk.sent_tokenize(SCREAMING_SNAKE_CASE    )    )





