The 'current quarter' report will be a bit more tricky as you will need to teach your QuickBase instance what a quarter is. But once you do that with a formula field, you can use the formula field in a filter to do the same.
I have an example of doing that with the 'Activity Request Date' field pictured above. I created a formula field called 'LS - Action Quarter' to calculate the quarter of this particular contract my 'LS - Action' occured. The formula is this ->
var Text monthNum = ToText(Month([Activity Request Date]));
If($monthNum="10" or $monthNum="11" or $monthNum="12","1st",
If($monthNum="1" or $monthNum="2" or $monthNum="3","2nd",
If($monthNum="4" or $monthNum="5" or $monthNum="6","3rd",
If($monthNum="7" or $monthNum="8" or $monthNum="9","4th",
If($monthNum="" or $monthNum=null,"No Activity Request Date Set for this Action.",
"Something Else we have not yet considered. Report this to Administration."
)))))
and looks like this in the Formula editor (easier to see what is going on)
Just pass in your date field where I have my 'Activity Request Date' and it should work.
Change the quarters to suit your fiscal or calendar or contractual needs.
This formula sets Oct, Nov, Dec - Quarter1 (1st)
Jan, Feb, Mar - 2nd
etc.
But this will only allow you to choose a quarter for your filter. You'll have to do some more teaching to get the system to know which quarter is 'current' automatically.
There is probably an easier way. Maybe someone will teach us both something. :)
Thanks,
~Rob