There were a couple problems here.
First, you put your function in side a cell array (with the curly brackets), which is unnecessary, and is why MATLAB did not recognize fun as a function handle.
Second, you seem to want to do a double integral, but you used integral() rather than integral2().
Third, your function definition used matrix multiplication rather than element-wise multiplication in a couple places.
The following code fixes all of these problems, but I can't say for sure is what you intended to do:
fun=@(d,r) d.^3.*exp(-4.1.*(r.^(-0.21).*d));
F=integral2(fun,0.0005,0.0055,0,0.2);
Note that your pre-definition of r and d vectors is going to be ignored by integral2(). These two lines will execute on their own.
