



_lowercase     							=						'''Input must be a string of 8 numbers plus letter'''
_lowercase     							=						'''TRWAGMYFPDXBNJZSQVHLCKE'''






def      _A				(UpperCamelCase		:      List[str] )  ->Dict:



			'''simple docstring'''







			if not isinstance(__A      ,			__A ):
						lowerCamelCase__ :      Optional[Any]								=		f"Expected string as input, found {type(__A ).__name__}"
						raise TypeError(__A )

			lowerCamelCase__ :      Any								=		spanish_id.replace("""-"""      ,			"""""" ).upper()
			if len(__A ) != 9:
						raise ValueError(__A )

			try:
						lowerCamelCase__ :      List[Any]								=		int(spanish_id_clean[0:8] )
						lowerCamelCase__ :      Any								=		spanish_id_clean[8]
			except ValueError as ex:
						raise ValueError(__A ) from ex

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

			return letter == LOOKUP_LETTERS[number % 23]


if __name__ == "__main__":
				import doctest

				doctest.testmod()








from math import factorial, pi






def      _A				(UpperCamelCase		:      float      ,			UpperCamelCase		:      int = 30 )  ->float:



			'''simple docstring'''







			if not isinstance(UpperCamelCase      ,			(int, float) ):
						raise ValueError("""maclaurin_sin() requires either an int or float for theta""" )

			if not isinstance(UpperCamelCase      ,			UpperCamelCase ) or accuracy <= 0:
						raise ValueError("""maclaurin_sin() requires a positive int for accuracy""" )

			lowerCamelCase__ :      Dict								=		float(UpperCamelCase )
			lowerCamelCase__ :      int								=		theta // (2 * pi)
			theta -= 2 * div * pi
			return sum(
			    (-1) ** r * theta ** (2 * r + 1) / factorial(2 * r + 1 ) for r in range(UpperCamelCase ) )






def      _A				(UpperCamelCase		:      float      ,			UpperCamelCase		:      int = 30 )  ->float:



			'''simple docstring'''







			if not isinstance(UpperCamelCase      ,			(int, float) ):
						raise ValueError("""maclaurin_cos() requires either an int or float for theta""" )

			if not isinstance(UpperCamelCase      ,			UpperCamelCase ) or accuracy <= 0:
						raise ValueError("""maclaurin_cos() requires a positive int for accuracy""" )

			lowerCamelCase__ :      int								=		float(UpperCamelCase )
			lowerCamelCase__ :      Optional[int]								=		theta // (2 * pi)
			theta -= 2 * div * pi
			return sum((-1) ** r * theta ** (2 * r) / factorial(2 * r ) for r in range(UpperCamelCase ) )


if __name__ == "__main__":
				import doctest

				doctest.testmod()

				print(maclaurin_sin(10))
				print(maclaurin_sin(-10))
				print(maclaurin_sin(10, 15))
				print(maclaurin_sin(-10, 15))

				print(maclaurin_cos(5))
				print(maclaurin_cos(-5))
				print(maclaurin_cos(10, 15))
				print(maclaurin_cos(-10, 15))



