I think you definitely should show Wolfram|Alpha to them, and you should take the opportunity to explain why such tools will never be a replacement for mathematical thinking.

Personally I found Mathematica extremely useful for learning calculus some 15 years ago (Wolfram|Alpha didn't exist at that time). It makes it easy to plot functions, check results, and encourages good students to experiment and learn. Graphics can be fun and will encourage students to do such things as trying to figure out the parametric equation of a sphere or torus even before they study it.

But it is also important to understand that such tools cannot replace thinking about the problem. I am quite active on Mathematica.SE and I often see people (presumably students) ask questions such as "Why doesn't Mathematica solve this equation?", "Why won't it compute this integral?", "Why won't it simplify this expression?", "Why does it give such a complicated result, I need a simple one!" They seems to treat it as a magic box that just gives solutions, and when it doesn't, they feel stuck. They don't think about such issues as: is the equation still solvable is this parameter is negative or complex? Does it at all make sense to use the (the complex and expensive to evaluate) closed form solution of this 4th order equation in my code, or should I solve the equation numerically? Does the number of roots to this function depend on the parameter values? Can one reasonable expect a closed form solution at all? Why do I want an analytical solution at all? Should I use approximations when solving this physics problem?

Mathematica can solve quartic equations, but does this really look like a useful result? This is the kind of result a blind "solve this for me, W|A!!" will give to students. Or should one look at this instead?

I believe that as their teacher, you owe it to your students to explain the proper use of computer algebra systems and explain why they will never replace thinking for yourself. If anything is unethical, it is allowing them to fall into this trap and treat this tool as some sort of magical oracle.

I think you definitely should show Wolfram|Alpha to them, and you should take the opportunity to explain why such tools will never be a replacement for mathematical thinking.

Personally I found Mathematica extremely useful for learning calculus some 15 years ago (Wolfram|Alpha didn't exist at that time). It makes it easy to plot functions, check results, and encourages good students to experiment and learn. Graphics can be fun and will encourage students to do such things as trying to figure out the parametric equation of a sphere or torus even before they study it.

But it is also important to understand that such tools cannot replace thinking about the problem. I am quite active on Mathematica.SE and I often see people (presumably students) ask questions such as "Why doesn't Mathematica solve this equation?", "Why won't it compute this integral?", "Why won't it simplify this expression?", "Why does it give such a complicated result, I need a simple one!" They seems to treat it as a magic box that just gives solutions, and when it doesn't, they feel stuck. They don't think about such issues as: is the equation still solvable is this parameter is negative or complex? Does it at all make sense to use the (the complicated and expensive to evaluate) closed form solution of this 4th order equation in my code, or should I solve the equation numerically? Does the number of roots to this function depend on the parameter values? Can one reasonable expect a closed form solution at all? Why do I want an analytical solution at all? Should I use approximations when solving this physics problem?

Mathematica can solve quartic equations, but does this really look like a useful result? This is the kind of result a blind "solve this for me, W|A!!" will give to students. Isn't this explanation so much more informative and useful?

I believe that as their teacher, you owe it to your students to explain the proper use of computer algebra systems and explain why they will never replace thinking for yourself. If anything is unethical, it is allowing them to fall into this trap and treat this tool as some sort of magical oracle.