


def   _lowercase(					__a				:						Optional[Any]    ,     __a				:						Optional[int]     ):
							# "extended trapezoidal rule"
							# int(f) = dx/2 * (f1 + 2f2 + ... + fn)
							a__      =(boundary[1] - boundary[0]) / steps
							a__      =boundary[0]
							a__      =boundary[1]
							a__      =make_points(__a    ,     __a    ,     __a     )
							a__      =0.0
							y += (h / 2.0) * f(__a     )
							for i in x_i:
														# print(i)
														y += h * f(__a     )
							y += (h / 2.0) * f(__a     )
							return y






def   _lowercase(					__a				:						Tuple    ,     __a				:						str    ,     __a				:						Union[str, Any]     ):
							a__      =a + h
							while x < (b - h):
														yield x
														a__      =x + h






def   _lowercase(					__a				:						Dict     ):  # enter your function here
							a__      =(x - 0) * (x - 0)
							return y






def   _lowercase(					):
							a__      =0.0  # Lower bound of integration
							a__      =1.0  # Upper bound of integration
							a__      =10.0  # define number of steps or resolution
							a__      =[a, b]  # define boundary of integration
							a__      =method_a(__a    ,     __a     )
							print(f"""y = {y}"""     )


if __name__ == "__main__":
	main()







from __future__ import annotations

from fractions import Fraction




def 		lowerCAmelCase_ (						lowerCamelCase						,  lowerCamelCase ):
				return (
				    num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
				)




def 		lowerCAmelCase_ (						lowerCamelCase ):
				__magic_name__						:						List[str]										=[]
				__magic_name__						:						List[Any]										=11
				__magic_name__						:						Tuple										=int("""1""" + """0""" * digit_len )
				for num in range(lowerCamelCase						,  lowerCamelCase ):
								while den <= 99:
												if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
																if is_digit_cancelling(lowerCamelCase						,  lowerCamelCase ):
																				solutions.append(F"{num}/{den}" )
												den += 1
								num += 1
								__magic_name__						:						List[str]										=10
				return solutions




def 		lowerCAmelCase_ (						lowerCamelCase = 2 ):
				__magic_name__						:						str										=1.0
				for fraction in fraction_list(lowerCamelCase ):
								__magic_name__						:						int										=Fraction(lowerCamelCase )
								result *= frac.denominator / frac.numerator
				return int(lowerCamelCase )


if __name__ == "__main__":
							print(solution())




