Actually, you don't need to interpolate the variable, and it's much safer not to:

my $module = "Digest::MD5";
eval 'use $module'; # note single quotes
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That's because use $var actually works. You just have to somehow populate $var before the compile-time effect of use takes place. A BEGIN block lets you do that. Silly example:

my $module;
BEGIN { $module = "Digest::MD5"; }
use $module;
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Note that the snippets of course aren't equivalent — the first loads the module at runtime, the second loads it at compile time.