Can't use mysql's curdate() as bind variable?

[Jonathan Mangin]

curdate() works if $edate is embedded directly in my
sql statement, but not as a bind variable. $bdate works
fine.

my $bdate = $q->param('bdate') || '%';
my $edate = $q->param('edate') || 'curdate()';

my $sql = "create table $temp_tbl
           (date date,
           uid varchar(14))
           engine = memory
           select date,
           ? as uid
           from calendar
           where date between ? and $edate";
my $sth = $dbh->prepare($sql);
$sth->execute($uid, $bdate) || die $sth->errstr();

It's mostly just irritating.
Am I doing something wrong?

Thanks,
Jon