Numerical integration: Simpson and trapezoidal method

[David Lucas]

Hello,

i've been looking for how to perform a numerical integration with the Simpson's Rule and i found it:

e.g.:

function y = f(x)

y = sqrt(sin(x))

endfunction

quadv("f", 1, pi/2)

It gives me the result of the integration of sqrt(sin(x)) from 1 to PI/2.

The problem is that i also want to set the number of sub-intervals.

In Maple i would do it like this(4 sub-intervals/partitions):

ApproximateInt(sqrt(sin(x)), x = 1 .. 3.141592654*(1/2), method = simpson, partition = 4)

What about trapezoidal method? Does trapz have the same syntax as quadv?

Also, is there any way to plot something like Maple does with the following sentence?:

ApproximateInt(sqrt(sin(x)), x = 1 .. 3.141592654*(1/2), method = simpson, partition = 4, output = plot)

Result: http://img148.imageshack.us/img148/2031/dibujoqw.jpg

Thank you.