Mon Mar  2 21:11:30 2020 

midpt_test
  R version 3.4.4 (2018-03-15) 
  midpt estimates an integral using the midpoint method.

  f(x) = x^2

  midpt ( f,  0 , 1 , m =  2  ) =  0.3125 
  midpt ( f,  0 , 1 , m =  10  ) =  0.3325 
  midpt ( f,  0 , 1 , m =  100  ) =  0.333325 
  midpt ( f,  0 , 1 , m =  1000  ) =  0.3333332 

midpt_test
  Normal end of execution.
Mon Mar  2 21:11:30 2020