If I might suggest, your goal is actively a poor one. Why?
Simpson's rule is a higher order rule. It tries to give you a higher degree of accuracy. However, the idea of introducing what is essentially multiple points of non-differentiability into your function will kill any gains you would have achieved using the higher order nature of Simpson's rule. There is simply no purpose in using Simpson's rule on a function that is not well behaved to gain from the higher order.
So first, just use trapezoidal rule.
Next, are you asking to sum only the part of your function value that does not exceed 10? That is, if the function is larger than 10, will you just use 10 at that point? Or will you not integrate at all over any region where the function value is greater than 10? These two are VERY different goals, and will have very different results.