try:
insert into aTable select max(a)^2, 'name' from aTable;
or
insert into aTable select max(a)^2, 'name' from aTable group by B;
If you need a join, you can do this:
insert into aTable select max(a)^2, 'name' from aTable, bTable;
My “Server version” is “5.0.51b-community-nt MySQL Community Edition (GPL)”