

'''simple docstring'''
_lowerCamelCase      					=     "Input must be a string of 8 numbers plus letter"
_lowerCamelCase      					=     "TRWAGMYFPDXBNJZSQVHLCKE"


def  a__       (    _SCREAMING_SNAKE_CASE   :       str				)     ->					Union[str, Any]:


	"""simple docstring"""





	if not isinstance(UpperCamelCase__	,				UpperCamelCase__				):
		UpperCAmelCase_     :      Optional[int]						=  F'''Expected string as input, found {type(UpperCamelCase__				).__name__}'''
		raise TypeError(UpperCamelCase__				)

	UpperCAmelCase_     :      Dict						=  spanish_id.replace("-"	,				""				).upper()
	if len(UpperCamelCase__				) != 9:
		raise ValueError(UpperCamelCase__				)

	try:
		UpperCAmelCase_     :      Union[str, Any]						=  int(spanish_id_clean[0:8]				)
		UpperCAmelCase_     :      Optional[Any]						=  spanish_id_clean[8]
	except ValueError as ex:
		raise ValueError(UpperCamelCase__				) from ex

	if letter.isdigit():
		raise ValueError(UpperCamelCase__				)

	return letter == LOOKUP_LETTERS[number % 23]


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							):


	"""simple docstring"""

	# A local function to see if a dot lands in the circle.
	def is_in_circle(UpperCamelCase__					: float     ,       UpperCamelCase__					: float							) -> 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(UpperCamelCase__							)							)
	# 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    lowerCAmelCase       (		UpperCamelCase__					: int     ,       UpperCamelCase__					: Callable[[float], float]     ,       UpperCamelCase__					: float = 0.0     ,       UpperCamelCase__					: float = 1.0     ,       ):


	"""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							):


	"""simple docstring"""

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

	__UpperCAmelCase      					=      area_under_curve_estimator(
	    UpperCamelCase__     ,       UpperCamelCase__     ,       UpperCamelCase__     ,       UpperCamelCase__							)
	__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    lowerCAmelCase       (		UpperCamelCase__					: int							):


	"""simple docstring"""

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

	__UpperCAmelCase      					=      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()
