May I use TPS75003 to power Spartan-6 XC6SLX45T?

The TPS75003 contains two 3A buck controllers and one 300mA LDO.  The Spartan-6 XC6SLX45T requires three outputs, one at 800mA, one at 1.5A, and one at 3A.  When the FPGA runs a full current, the TPS75003 is NOT capable of providing the required power.  If your customer operates the Spartan-6 so that the required currents can be supplied by the TPS75003, then you can use the TPS75003 as the power source.

Note that TI's processor attach page provides several reference designs for this processor and many more.  My suggestion is to use one of the existing designs found at

http://focus.ti.com/analog/docs/powerhome.tsp?familyId=64&contentType=4&DCMP=TIHomeTracking&HQS=Other+OT+home_p_power