






def 			lowercase__  (				A_:	int     ,			A_:	int		)  ->							int:







       """simple docstring"""






       __UpperCAmelCase    							=1.0
       for i in range(1     ,			r + 1		):
              ret *= (n + 1 - i) / i
       return round(A_		)







def 			lowercase__  (				A_:	int		)  ->							int:







       """simple docstring"""






       return choose(8 + n     ,			A_		) + choose(9 + n     ,			A_		) - 10







def 			lowercase__  (				A_:	int		)  ->							int:







       """simple docstring"""






       return sum(non_bouncy_exact(A_		) for i in range(1     ,			n + 1		)		)







def 			lowercase__  (				A_:	int = 100		)  ->							int:







       """simple docstring"""






       return non_bouncy_upto(A_		)


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












import math as m







def 			lowercase__  (				A_:	Tuple     ,			A_:	str     ,			A_:	Union[str, Any]=0.0_0_1		)  ->							List[str]:







       """simple docstring"""






       return (f(a + h		) - f(a - h		)) / (2 * h)







def 			lowercase__  (				A_:	str     ,			A_:	Union[str, Any]=0     ,			A_:	List[Any]=100     ,			A_:	Optional[Any]=0.0_0_0_1     ,			A_:	Tuple=1e-6     ,			A_:	Union[str, Any]=False		)  ->							Union[str, Any]:







       """simple docstring"""






       __UpperCAmelCase    							=xa  # set the initial guess
       __UpperCAmelCase    							=[a]
       __UpperCAmelCase    							=abs(f(A_		)		)
       __UpperCAmelCase    							=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"""		)
              __UpperCAmelCase    							=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

   __A  							=  lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
   __A							,    __A							,    __A  							=  newton_raphson(
       f, xa=10, maxiter=10_00, 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}}}""")




