You can do this, as well as interpolation in more normal double-quoted strings, with the module Interpolation, originally written by dominus as a joke, currently maintained by Jenda.

I don't like the import interface, I think you should just call a tie a tie, but you can just use tie with the module without any changes.

use Interpolation;
tie my %EVAL, Interpolation => 'eval';
# or: tie my %EVAL, Interpolation => sub { shift };
print <<"END";
The sum of 3 and 4 is $EVAL{3+4}.
END
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(Be sure to have at least one more line under "END")

The key to how this works is that an index to a hash or an array is always interpreted as perl code. Next, a tied hash is used to execute an associated function, instead of actually fetching a hash value out of somewhere.