Return Functions from parallel execution of module

I wrote a module which numerically solves an ODE using NDSolve. The result from this is e.g. either InterpolatingFunction[{{0.,1000.}},<>][t] or InterpolatingFunction[{{0.,1000.}},<>][t$1062], depending whether the independent varialbe t is global or local in the module.

So far, I didn't care that it is global and everything worked fine. As this is imho is a source of upcoming trouble, I would like to switch to the local variable-version. As therefore I can't use a replacement rule like InterpolatingFunction[{{0.,1000.}},<>][t] /. t->3 to extract single values or to plot the function any more, I tried to wrap it into a function as the following minimal example demonstrates.

compute[] := Module[{res, f},
   points = Table[{x, x}, {x, 0, 10}];
   res = Interpolation[points];
   f[x_] := res[x];
   f
];

Using this code works fine.

In[109]:= ex = compute[];
          ex[3]
Out[110]= 3

I now want to run this computation with different parameters so I put it into a ParallelTable. The resulting list then does not contain the correct functions anymore but only their symbols.

In[111]:= a = ParallelTable[compute[], {i, 0, 100}];
          a[[1]][3]

Out[112]= f$1870[3]

Note that this works perfectly when ParallelTable is replace by a normal Table.

Can you explain to me why this happens? Has this something to do with the definitions of the functions "living" on the sub-kernels and not being passed back to the main kernel?

Edit

Another aspect of the problem, a solution to which would help me too, is the following. If I multiply the InterpolatingFunction by a number and try to then extract values from it, it doesn't work as I would expect. Using the above example and assuming tha res is returned (indicated by the use of res in the following).

In[150]:= fcn=5*res;
          fcn[3]

Out[151]= (5 InterpolatingFunction[{{0,10}},<>])[3]

Is there maybe a workaround for this?