Do you calculate F in fcoeff? If so, you can make it a global variable and it will retain its value between calls to fcoeff.
One complicating factor is that the parabolic function uses the variable time step ODE solver, ode15s, internally. So fcoeff gets called at unevenly-spaced and possibly non-monotonically increasing time points. You may need to save several values of F along with the times where they are computed and select a particular one or interpolate between values to obtain the value of F you need.