"""simple docstring"""




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






def   UpperCAmelCase					(	UpperCamelCase__				):






							"""simple docstring"""





							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(UpperCamelCase__				)				)
							# 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       ,    ):






							"""simple docstring"""





							return mean(
							    function_to_integrate(uniform(UpperCamelCase__       ,    UpperCamelCase__				)				) for _ in range(UpperCamelCase__				)				) * (max_value - min_value)






def   UpperCAmelCase					(	UpperCamelCase__       ,    UpperCamelCase__ = 0.0       ,    UpperCamelCase__ = 1.0				):






							"""simple docstring"""





							def identity_function(UpperCamelCase__				) -> float:
														return x

							A__	     =							area_under_curve_estimator(
							    UpperCamelCase__       ,    UpperCamelCase__       ,    UpperCamelCase__       ,    UpperCamelCase__				)
							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__				):






							"""simple docstring"""





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

							A__	     =							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()






"""simple docstring"""




import os


# All paths are set with the intent you should run this script from the root of the repo with the command
# python utils/check_doctest_list.py
__lowerCamelCase											=  "."


if __name__ == "__main__":
				__lowerCamelCase											=  os.path.join(REPO_PATH, "utils/documentation_tests.txt")
				__lowerCamelCase											=  []
				__lowerCamelCase											=  []
				with open(doctest_file_path) as fp:
								for line in fp:
												__lowerCamelCase											=  line.strip()
												__lowerCamelCase											=  os.path.join(REPO_PATH, line)
												if not (os.path.isfile(path) or os.path.isdir(path)):
																non_existent_paths.append(line)
												all_paths.append(path)
				if len(non_existent_paths) > 0:
								__lowerCamelCase											=  "\n".join(non_existent_paths)
								raise ValueError(F'''`utils/documentation_tests.txt` contains non-existent paths:\n{non_existent_paths}''')
				if all_paths != sorted(all_paths):
								raise ValueError("Files in `utils/documentation_tests.txt` are not in alphabetical order.")





