It seems like the calculator is true to its name in that it only evaluates the given input function. Whether or not a function is monotonic should have no bearing on the calculator because it isn't actually solving anything, only evaluating. The solution method takes place in the user's mind and so the user would need to recognize that a given equality may be untrue (that is, the problem is unsolvable) but this would manifest in the user being unable to drive two equations to a single answer.

For example, if the user had sin(x)+1=2 and x^2=4 (or, sin(x)+1=x^2-4 equivalently) then the lines would be set up as

sin(3)+1 = eval

3^2 = eval

and then the user would link the two 3s and proceed to "scrub" until a common answer for x was found. While this problem is unsolvable for x, each expression is valid and able to be evaluated.

As somebody said below, this scrubbing amounts to nothing more than brute force guess and check of equations. No additional knowledge is gained through this type of approach and I would never recommend this for anything but the most trivial of problems and even then a standard approach would probably be faster.

EDIT: Looking at the more advanced "locking" functionality, I think you are probably correct in that this functionality may be constrained to monotonic functions only.

I wonder. Specifically, would you be able to "scrub" every number in the "equation" 1 beans / 1 buckets = 1 beans per bucket?

Uh, what about this doesn't work for any solvable equation?