calculating user defined formulas (with c++)

If it will be used frequently and if it will be extended in the future, I would almost recommend adding either Python or Lua into your code. Lua is a very lightweight scripting language which you can hook into and provide new functions, operators etc. If you want to do more robust and complicated things, use Python instead.

You can represent your formula as a tree of operations and sub-expressions. You may want to define types or constants for Operation types and Variables.

You can then easily enough write a method that recurses through the tree, applying the appropriate operations to whatever values you pass in.