





from __future__ import annotations







def  A					(				UpperCAmelCase					):
					_snake_case							:       int
					_snake_case							:       list[str]												= list(UpperCAmelCase					)
					_snake_case							,			_snake_case							:       Any												= _vector[:-1], int(_vector[-1]					)
					_snake_case							:       list[int]												= [int(UpperCAmelCase					) for digit in __vector]

					vector.reverse()
					for i, digit in enumerate(UpperCAmelCase					):
										if i & 1 == 0:
															_snake_case							:       int												= digit * 2
															if doubled > 9:
																				doubled -= 9
															check_digit += doubled
										else:
															check_digit += digit

					return check_digit % 10 == 0


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							assert is_luhn('79927398713')
							assert not is_luhn('79927398714')






def  A					(				UpperCAmelCase	,	UpperCAmelCase					):
					# "Simpson Rule"
					# int(f) = delta_x/2 * (b-a)/3*(f1 + 4f2 + 2f_3 + ... + fn)
					_snake_case							:       List[str]												= (boundary[1] - boundary[0]) / steps
					_snake_case							:       List[Any]												= boundary[0]
					_snake_case							:       Tuple												= boundary[1]
					_snake_case							:       str												= make_points(UpperCAmelCase	,	UpperCAmelCase	,	UpperCAmelCase					)
					_snake_case							:       str												= 0.0
					y += (h / 3.0) * f(UpperCAmelCase					)
					_snake_case							:       Tuple												= 2
					for i in x_i:
										y += (h / 3) * (4 - 2 * (cnt % 2)) * f(UpperCAmelCase					)
										cnt += 1
					y += (h / 3.0) * f(UpperCAmelCase					)
					return y







def  A					(				UpperCAmelCase	,	UpperCAmelCase	,	UpperCAmelCase					):
					_snake_case							:       Union[str, Any]												= a + h
					while x < (b - h):
										yield x
										_snake_case							:       Optional[Any]												= x + h







def  A					(				UpperCAmelCase					):  # enter your function here
					_snake_case							:       Dict												= (x - 0) * (x - 0)
					return y







def  A					(				):
					_snake_case							:       int												= 0.0  # Lower bound of integration
					_snake_case							:       Union[str, Any]												= 1.0  # Upper bound of integration
					_snake_case							:       List[str]												= 1_0.0  # define number of steps or resolution
					_snake_case							:       Optional[int]												= [a, b]  # define boundary of integration
					_snake_case							:       List[str]												= method_a(UpperCAmelCase	,	UpperCAmelCase					)
					print(F"""y = {y}"""					)


if __name__ == "__main__":
							main()