B737-300 MAX GROSS TKOF RWY 35R CLBING TO 10000 FT. COMPLETING AFTER TKOF CHKLIST AND VECTORED TO 100 DEGS PLUS TA GIVEN. AUTOPLT WOULD NOT ENGAGE AND NOTED ALT 10150 FT CLBING. DSNDED TO 9900 FT WHEN CTLR QUESTIONED ALT. TCASII TA AND RA AND SAW TFC VISUALLY 500 FT ABOVE. WHEN CLR OF TFC CLRED TO 16000 FT.

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WE WERE MAKING A MAX GROSS WT TKOF ON RWY 35R AT COS USING IMPROVED CLB; BLEEDS OFF; FLAPS 1 DEG. THE CLRNC WAS RWY HEADING CLB TO 10000 FT MSL. AFTER LIFT-OFF I PROCEEDED ON RWY HEADING AND THE TWR TOLD US TO TURN TO 010 DEGS AND CONTACT DEP CTL. THE ACFT WAS BEING CLEANED UP AS WE CONTACTED DEP. HE GAVE US A TURN TO 100 DEGS TO INTERCEPT THE 349 DEG RADIAL OFF PUB. I CALLED FOR THE AFTER TKOF CHKLIST AND RESET THE BLEEDS AS WE LEVELED AT 10000 FT TURNING TO 100 DEGS. DEP CTL ADVISED US OF VFR TFC AT 2 O'CLOCK. THE COPLT WAS LOOKING FOR TFC AS I ATTEMPTED TO ENGAGE THE AUTOPLT. IT WOULD NOT ENGAGE SO I ATTEMPTED IT AGAIN WITHOUT SUCCESS. I LOOKED BACK AT THE ALTIMETER AND NOTICED WE WERE AT 10150 FT IN A CLB. I IMMEDIATELY PUSHED THE NOSE DOWN TO REGAIN 10000 FT. AT THIS TIME DEP CTL ASKED IF WE WERE CLBING BECAUSE OF A POSSIBLE CONFLICT WITH THE VFR TFC. BY THIS TIME WE WERE AT EXACTLY 9900 FT SO WE TOLD HIM WE WERE AT 10000 FT. WE THEN PICKED UP THE TFC VISUALLY AND ON TCASII; WHICH SHOWED HIM AT 500 FT ABOVE US CLOSING. SOON AFTERWARD WE GOT A TA FOLLOWED BY AN RA FROM THE TCASII. WE STAYED AT 9900 FT UNTIL HE PASSED BECAUSE WE HAD HIM VISUALLY. DEP CTL THEN GAVE US A CLB TO 16000 FT AND CONTACT ZDV. LOOKING BACK I SHOULD HAVE EITHER ENGAGED THE AUTOPLT EARLIER TO REDUCE THE WORKLOAD OR WAITED TILL WE HAD BEEN CLRED TO CLB TO 16000 FT. THERE IS JUST TOO MUCH GOING ON IN THE ATA ESPECIALLY WHEN VFR ACFT ARE FLYING OVER THE TOP.