Lookup and multiple criteria
 

I have an spreadsheet with columns like:

col A col D col E colF
B230 8 1 0
F001 -5 0 10
F002 3 20 0
F010 5 -29 3
F014 40 3 7
F020 -25 -6 -100
F113 0 0 0
H002 34 -50 23
in ascendent order.
I want to be able to Sum col D to colF if colA is between F001 and F020
except F010.
I am just starting with this and I really don't know how to mix and match
all the formulas. any help will be much appreaciated!!