This works:

while ($str =~ s/~~(\$.+?)~~/__TOKEN__/) {
    my $val = eval $1;
    $str =~ s/__TOKEN__/$val/;
}
[download]

There is probably a more efficient way to do it, but this does the job. $str can be each individual line, or whole chunks of the HTML.

Update: a better way, as suggested by ikegami...

$str =~ s/~~(\$.+?)~~/eval $1/ge;
[download]

I wonder how s///e evaded my notice for so long.