It needs to be
=SUMPRODUCT((A7:A180>=DATE(2011,05, 01))*(A7:A180<=DATE(2011, 05, 03)))
or
=SUMPRODUCT((A7:A180>=DATE(Year(date from cell),Month(date from cell),Day(date from cell)))*(A7:A180<=DATE(Year(date to cell),Month(date to cell),Day(date to cell))))
Where Date From Cell and Date to Cell are cell references eg: D1 etc