I agree, eval seems unneeded here. You can still use s///, although I would prefer it like yours.

#!/usr/bin/perl

my $x = "Line1\nLine2Resolved 200 problems out of 5000 picked\nLine4\n
+Line5";
$x =~ s/.*?Resolved (\d+) problems out of (\d+) picked.*/
       ($2 - ($1\/$2)) > .5 ? 1 : 0 /es;

print "$x\n";
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Remember to escape the division in the substitution.

qq