Fully Parametric Box

I made corners more round as the wall thinkness is constant there too.
The lid is not optional. lid_height = 0 means no lid.

Edit: wall_thickness should be an even product of the nozzle width for optimun path. At least with Cura wall_thickness = 1.2 with 0.4 nozzle created a lot of travels and many of them without retraction. With wall_thickenss = 0.8 this does not happen.

Edit2: It seems some corner issues (to get perfect parallel paths) are sometimes there with either cura or slic3r. It depends on the wall_thickness and slicer software.

v3: Now radius define the outer radius of the bottom part. The inner radius is less and the lid radius is more. So all the walls have even thickness and the inner radius of the lid matches the outer radius of the body and all the perimeter matches perfectly.