



import math as m






def 			__lowercase     (				a__							,     a__							,     a__=0.001     )       ->				Union[str, Any]:
							return (f(a + h     ) - f(a - h     )) / (2 * h)






def 			__lowercase     (				a__							,     a__=0							,     a__=1_00							,     a__=0.0001							,     a__=1E-6							,     a__=False     )       ->				Union[str, Any]:
							__SCREAMING_SNAKE_CASE								=      xa  # set the initial guess
							__SCREAMING_SNAKE_CASE								=      [a]
							__SCREAMING_SNAKE_CASE								=      abs(f(a__     )     )
							__SCREAMING_SNAKE_CASE								=      lambda a__     : calc_derivative(a__							,     a__							,     h=a__     )  # noqa: E731  Derivative of f(x)
							for _ in range(a__     ):
														if fa(a__     ) == 0:
																					raise ValueError('No converging solution found'     )
														__SCREAMING_SNAKE_CASE								=      a - f(a__     ) / fa(a__     )  # Calculate the next estimate
														if logsteps:
																					steps.append(a__     )
														if error < maxerror:
																					break
							else:
														raise ValueError('Iteration limit reached, no converging solution found'     )
							if logsteps:
														# If logstep is true, then log intermediate steps
														return a, error, steps
							return a, error


if __name__ == "__main__":
			from matplotlib import pyplot as plt

			lowerCAmelCase__	:  Tuple 		=lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
			lowerCAmelCase__	:  Optional[int] 		=newton_raphson(
			    f, xa=10, maxiter=1000, step=1E-6, logsteps=True
			)
			plt.plot([abs(f(x)) for x in steps])
			plt.xlabel('''step''')
			plt.ylabel('''error''')
			plt.show()
			print(F'''solution = {{{solution:f}}}, error = {{{error:f}}}''')











from itertools import combinations, product






def 			__lowercase     (				a__							,     a__							,     a__							,     a__     )       ->				bool:
							if xa == ya == 0 or xa == ya == 0:
														return False
							__SCREAMING_SNAKE_CASE								=      xa * xa + ya * ya
							__SCREAMING_SNAKE_CASE								=      xa * xa + ya * ya
							__SCREAMING_SNAKE_CASE								=      (xa - xa) * (xa - xa) + (ya - ya) * (ya - ya)
							return (
							    a_square + b_square == c_square
							    or a_square + c_square == b_square
							    or b_square + c_square == a_square
							)






def 			__lowercase     (				a__ = 50     )       ->				int:
							return sum(
							    1
							    for pta, pta in combinations(product(range(limit + 1     )							,     repeat=2     )							,     2     )
							    if is_right(*a__							,     *a__     )     )


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






