Computational Sciences
A few examples of what you can ask Wolfram|Alpha about:
compute properties of an elementary cellular automaton
specify range and number of colors
specify a totalistic cellular automaton
compute properties of a Turing machine
specify initial conditions
name a famous Turing machine
get information about a complexity class
compare complexity classes
Ackermann Function
evaluate the Ackermann function
analyze an algebraic code
find codes with a given level of error correction
get usage information about a Wolfram Language function
find groups of functions
use functional programming constructs such as Map
compare programming languages
get information about a software product
compare software products