code: 
  
  
  
  
  
  
  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() = }""")
  
  
  
  
  
style_context: 
  
  
  
  
  
  
  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}}}""")
  
  
  
  
  