Carly Fiorina took the stage at the 2005 Consumer Electronics Show in Las Vegas to introduce a new camera from Hewlett-Packard Co., joined by singer Gwen Stefani, who shot a selfie with the beaming chief executive.

“I can’t believe I’m on stage with this woman,” said Ms. Stefani, who was introduced by Ms. Fiorina as H-P’s “hippest product engineer” for the singer’s help designing the camera’s case and accessories.

The...