Ahh yes, you've hit the bugaboo with using =>. It's very very very quotey. It quotes even subroutine names (as long as they are simply bare words), which is what a use constant ends up being. Either switch to comma instead of arrow, or invoke your subroutine:

my %capitol_map = (
    WISCONSIN() => "Madison",
    ILLINOIS()  => "Springfield",
    ...
);
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-- Randal L. Schwartz, Perl hacker
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