
'''simple docstring'''





def 							_lowerCamelCase			(					lowerCamelCase_:  List[str]				,	lowerCamelCase_:  str		):



				'''simple docstring'''







				if n < 0:
								return 0
				# table[i] represents the number of ways to get to amount i
				A     :  List[str]   =				[0] * (n + 1)

				# There is exactly 1 way to get to zero(You pick no coins).
				A     :  Tuple   =				1

				# Pick all coins one by one and update table[] values
				# after the index greater than or equal to the value of the
				# picked coin
				for coin_val in s:
								for j in range(lowerCamelCase_				,	n + 1		):
												table[j] += table[j - coin_val]

				return table[n]


if __name__ == "__main__":
					import doctest

					doctest.testmod()

UpperCamelCase_  =	10_00





def 							_lowerCamelCase			(					lowerCamelCase_:  float		):



				'''simple docstring'''







				return x * x





def 							_lowerCamelCase			(					lowerCamelCase_:  Tuple				,	lowerCamelCase_:  float				,	lowerCamelCase_:  float				,	lowerCamelCase_:  int = 4		):



				'''simple docstring'''







				assert callable(
				    lowerCamelCase_		), f"""the function(object) passed should be callable your input : {function}"""
				assert isinstance(lowerCamelCase_				,	(float, int)		), f"""a should be float or integer your input : {a}"""
				assert isinstance(function(lowerCamelCase_		)				,	(float, int)		), (
				    "the function should return integer or float return type of your function, "
				    f"""{type(lowerCamelCase_		)}"""
				)
				assert isinstance(lowerCamelCase_				,	(float, int)		), f"""b should be float or integer your input : {b}"""
				assert (
				    isinstance(lowerCamelCase_				,	lowerCamelCase_		) and precision > 0
				), f"""precision should be positive integer your input : {precision}"""

				# just applying the formula of simpson for approximate integration written in
				# mentioned article in first comment of this file and above this function

				A     :  Tuple   =				(b - a) / N_STEPS
				A     :  List[str]   =				function(lowerCamelCase_		) + function(lowerCamelCase_		)

				for i in range(1				,	lowerCamelCase_		):
								A     :  int   =				a + h * i
								result += function(lowerCamelCase_		) * (4 if i % 2 else 2)

				result *= h / 3
				return round(lowerCamelCase_				,	lowerCamelCase_		)


if __name__ == "__main__":
					import doctest

					doctest.testmod()