Casio fx-991EX vs Hp 50g speed difference

[Albert Chan]

Just learned there is a trick to use Romberg's method for periodic function:
Casio keisan on-line Romberg Integration calculator, option non-linear substitution

Code:

def nonlinear(f, a, b):
    c, d = (b-a)/4, (b+a)/2
    return lambda u, k=3*c: k*(1 - u*u) * f(c*u*(3-u*u) + d)

Just integrate above transformed f, from -1 to 1:

\(\int_0^{200}sin(x) dx \) = \(\int_{-1}^{1}150(1-u^2) sin[50u (3 - u^2) + 100] du \)

On my Casio FX-115MS, it had gotten the sin(x) integral wrong: -96.581

With transformed integral, after 3 minutes 45 seconds, I got 0.51281 :-)

Amazingly, Mathematica can solve the messy transformed integral symbolically: 2 (sin(100))^2