Educational Math Software What is the the most educational software for high school and college math?
Not the one that just gives you the answer, but has any of the following:
Edit: Software mentioned in answer added in brackets


*



*

*provides step-by-step solutions [WolframAlpha];

*can verify your step-by-step solution [empty];

*can give you hints [empty];

*can generate problems similar to given one [empty];


or something along those lines.

 A: Wolfram Alpha. Try, for instance "solve x^2-x-1=0" and click "show steps".
A: Maple can give step-by-step solutions as well as give hints on what rule you could apply next.
A: MathXpert supposedly fits your first 3 criteria (though I have never tried it).
A: There is Microsoft Math. I haven't actually used it, but I know that it can provide step by step solutions. Here's a nice review. Also it's $20.
A: Good educational software allows one to explore on one's own and at the same time provides problem solving tools. A very nice example of this, and its free, is:
http://www.geogebra.org/cms/
A: Geogebra at 
http://www.geogebra.org/cms/
free and multi-level
A: Also, Bagatrix has a suite of math software that shows you individual steps for math problems that it could solve. In my experience though, it is quite limited in what it can actually solve.
A: Algebrator (also called Softmath) is a computer algebra system (CAS), which was developed in the late 1990s by Neven Jurkovic of Softmath, San Antonio, Texas. It can show solution steps and context sensitive explanations.
A: Mathematical Assistant on Web.
This site can be used to solve various problems - mainly from calculus. For example, differentiation, integration, ODEs. When integrating, you can choose which substitution to use or which functions to use in integrating by parts.
EDIT: The website does not work at the moment. (I hope it will be back at some point.) There are some instructions how you can download and install the same software locally on your computer: http://user.mendelu.cz/tihlarik/maw/offline.html
A: Here is a small tool to help calculate the process of integrate.(It did can't work out all the integrate, but can help a bit.)
Require : Mathematica and Rubi
First, run this to install Rubi
PacletInstall["https://github.com/RuleBasedIntegration/Rubi/releases/download/4.16.1.0/Rubi-4.16.1.0.paclet"]

Second, run this to define a funcion.
<<Rubi`
IntWithStepsOfTeXForm[expr_, var_]:=With[{TeX2Str = Convert`TeX`ExpressionToTeX},
Steps[Int[expr, var], RubiPrintInformation -> False] //
Flatten //
Most //
Cases[RubiIntermediateResult[x_] :> "=&" <> (TeX2Str[HoldForm @@ x]) <>"\\\\"] //
{"\\begin{aligned}", TeX2Str@HoldForm@Int[expr, var], ##&@@#, "\\end{aligned}"} & //
StringReplace[{"\\, d"->"\\, \\mathrm{d}",  "\\int" -> "\\displaystyle \\int"}] //
StringRiffle]

Third: enjoy it :P
for example: if we want calculate $\int \sqrt{1+\sqrt{x}}\,dx$
IntWithStepsOfTeXForm[Sqrt[1 + Sqrt[x]], x] // Print

and we get:
\begin{aligned} \displaystyle \int \sqrt{1+\sqrt{x}} \, \mathrm{d}x =&2 \text{Subst}\left(\displaystyle \int x \sqrt{1+x} \, \mathrm{d}x,x,\sqrt{x}\right)\\ =&2 \text{Subst}\left(\displaystyle \int \left(-\sqrt{1+x}+(1+x)^{3/2}\right) \, \mathrm{d}x,x,\sqrt{x}\right)\\ =&-\frac{4}{3} \left(1+\sqrt{x}\right)^{3/2}+\frac{4}{5} \left(1+\sqrt{x}\right)^{5/2}\\ \end{aligned}

Which can be directly copied out and used.
$$
\begin{aligned} \displaystyle \int \sqrt{1+\sqrt{x}} \, \mathrm{d}x =&2 \text{Subst}\left(\displaystyle \int x \sqrt{1+x} \, \mathrm{d}x,x,\sqrt{x}\right)\\ =&2 \text{Subst}\left(\displaystyle \int \left(-\sqrt{1+x}+(1+x)^{3/2}\right) \, \mathrm{d}x,x,\sqrt{x}\right)\\ =&-\frac{4}{3} \left(1+\sqrt{x}\right)^{3/2}+\frac{4}{5} \left(1+\sqrt{x}\right)^{5/2}\\ \end{aligned}
$$
It's speed is very fast. And easy to use.
