After all of those comments, to be honest, sorry, but you were both working far too hard on a moderately simple problem.
Simplest is to just create a polygon, then use polyarea of that object. Alternatively, create a polyshape object. Again, compute the area of said polygonal region.
The result will be a piecewise linear approximation to the area. That is the same result you will get from trapz anyway, since trapz is simply a tool that performs integration using linear segments to connect the points.