$a =~ /$b/

##</code><code>##

$a =~ /\Q$b\E/

$a =~ /\Q$b/  # \E is optional

my $b_re = quotemeta($b);  # This is what \Q does
$a =~ /$b_re/

##</code><code>##

$a eq $b

$a =~ /^\Q$b\E\z/

my $b_re = quotemeta($b);
$a =~ /^$b_re\z/