in the eCart object, you need to create a shipping rule for each quantity break, using the Subtotal For Any Column trigger.
for example:
Name: 1 to 3 items
Triggers:
Subtotal For Any Column:
If the subtotal for column "Quantity" is ">=" a value of "1"
AND
Subtotal For Any Column:
If the subtotal for column "Quantity" is "<=" a value of "3"
Calculation:
Flat Rate "10"
create additional rules substituting the quantities and flat rate charges.