The worst aspect of tools like these is that the instructor can unintentionally create impossible problems. For example, even though the final answer may need only 3 significant digits, the details of the calculation might be such that far more digits are required to reach the final answer accurately; I had numerous occasions in college where such tools required in intermediate accuracy beyond the means of a standard calculator.
Generally, the numbers given in the problem statement are randomized (so that each student is given a slightly different problem). If the instructor is careless in coding the randomizer, nonsense can result. Case in point:
In my freshman engineering course, we were doing a section on statics. The professor set us a problem, via the web, as follows:
A helium balloon is tethered to the ground via three tethers, which are anchored at three points in the XY plane: (x1,y1), (x2,y2), (x3,y3). The balloon has a net buoyant force of F and is hovering in equilibrium over the point (x0,y0). (All specific numbers are randomized.) Find the tension in each of the three ropes, and the unit vectors along which each of these tensions act.
That's all well and good, except the vast majority of students (myself included) kept coming up with negative tensions, no matter how we tried to calculate them. We brought this up with the professor, and he told us we must have done it wrong, because "You can't push a rope" (he repeated this rather dogmatically). Sure, you can't push a rope, but you can write bad code for a problem that involves unphysical rope-pushing...
What had happened (and I had to demonstrate this with rigorous mathematics to the professor before he would back down and re-grade the problem) is that the random number generator was not taking into account the physics of the problem. All four points P1, P2, P3 and P0 were chosen independently. This meant that, the majority of the time, the point P0 was actually chosen such that it was outside the triangle formed by P1, P2, and P3. This would mean that, unless there were a wind pulling the balloon in that direction, at least one of the ropes must be in compression rather than tension in order to hold the balloon in place.
Thus, most of the class had actually done the problem correctly. They got an absurd result because the problem was coded to give them an absurd physical situation.
Moreover, this guy had required about 10 significant digits on the three unit vectors in Part B. I think what actually happened is that the code must have been checking for strict equality, using floating-point numbers, instead of using a small error bounds. Thus, it was often impossible to satisfy the precision required to get any points. (I remember quite often in this class that students would have to enter 10-12 digits in their answers all the time, and for no reason other than the professor was paranoid about cheating and guessing).
