




"""simple docstring"""




def       __UpperCAmelCase      (				__UpperCamelCase = 30					):
			__lowercase	:       List[str]				=   exponent + 2
			__lowercase	:       Any				=   (1 + 5**0.5) / 2
			__lowercase	:       Any				=   (phi**fibonacci_index - (phi - 1) ** fibonacci_index) / 5**0.5

			return int(__UpperCamelCase					)


if __name__ == "__main__":
							print(F"{solution() = }")









"""simple docstring"""




from collections.abc import Callable

a_            =   Callable[[float], float]  # type alias for a real -> real function







def       __UpperCAmelCase      (				__UpperCamelCase					,							__UpperCamelCase					,							__UpperCamelCase					,							):
			__lowercase	:       str				=   float(__UpperCamelCase					)
			while True:
						try:
									__lowercase	:       Dict				=   prev_guess - function(__UpperCamelCase					) / derivative(__UpperCamelCase					)
						except ZeroDivisionError:
									raise ZeroDivisionError('''Could not find root'''					) from None
						if abs(prev_guess - next_guess					) < 10**-5:
									return next_guess
						__lowercase	:       List[Any]				=   next_guess







def       __UpperCAmelCase      (				__UpperCamelCase					):
			return (x**3) - (2 * x) - 5







def       __UpperCAmelCase      (				__UpperCamelCase					):
			return 3 * (x**2) - 2


if __name__ == "__main__":
			print(newton(f, fa, 3))



