Question: how can I use dsolve/numeric with a numerical integration in the D.E. system?

I am facing a problem dsolve/numeric, and I am attaching two files: dsolve-issue.mws and dsolve-issue2.mws the first one shows a simplified version of the problem, the second one is an actual example of one the DE systems I desperately need to solve. There are brief comments in the files describing the problem, but here is the summary:


lets say we have the following differential equation:

 diff(x(t),t)= Int( f(x(t),p), p=p1..p2);

where p1 and p2 are real numbers, and f(x,p) is a function that cannot be integrated analatically [ that's why I used Int() instead of int() ]. However, assume that maple can integrate the right side numerically with no problems. In principle, maple should be able to solve this differential equation numerically, but no matter how hard I try to rewrite it in a friendly way for maple, it fails to do it.

looking at older questions and posts, i found a thread that solves the opposite of my problem, where it was explained how to numerically integrate the result of the dsolve/numeric. Note that what I am trying to do here is the exact opposite, numerically integrate the terms in the differential equaiton before solving it numerically at each point. here is the link to that post.

I wrote my own simple code in maple to numerically solve the system with a second order Runge-Kutta method, but it is extremely slow, and not accurate enough to say the least, but it wroks in general. I just wanted to see that maple in principle should be able to do it.

any help would be greatly appreciated.

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