





from math import factorial, pi

def       A(__a:			float						,   __a:			int = 30				):





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

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

		lowerCAmelCase_												=				float(lowerCamelCase_				)
		lowerCAmelCase_												=				theta // (2 * pi)
		theta -= 2 * div * pi
		return sum(
		    (-1) ** r * theta ** (2 * r + 1) / factorial(2 * r + 1				) for r in range(lowerCamelCase_				)				)

def       A(__a:			float						,   __a:			int = 30				):





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

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

		lowerCAmelCase_												=				float(lowerCamelCase_				)
		lowerCAmelCase_												=				theta // (2 * pi)
		theta -= 2 * div * pi
		return sum((-1) ** r * theta ** (2 * r) / factorial(2 * r				) for r in range(lowerCamelCase_				)				)


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))







def        __UpperCAmelCase						(							lowerCamelCase_ :     List[str]  ,							lowerCamelCase_ :     Optional[Any]  )       ->  int:







			"""simple docstring"""





			SCREAMING_SNAKE_CASE_   : List[Any]					  =      [0 for i in range(r + 1  )]
			# nc0 = 1
			SCREAMING_SNAKE_CASE_   : Dict					  =      1
			for i in range(1  ,							n + 1  ):
						# to compute current row from previous row.
						SCREAMING_SNAKE_CASE_   : Optional[int]					  =      min(lowerCamelCase_  ,							lowerCamelCase_  )
						while j > 0:
									c[j] += c[j - 1]
									j -= 1
			return c[r]




print(binomial_coefficient(n=10, r=5))



