Quick, give me a word which means this (NOT a game, for once

How about “stiff” ?

Rigid, yet flexible? That sounds quite penile to me.

Don’t tempt me. I might actually put that word into the document if anybody else gives me work today.

Semi-erect.

Tensile is in engineering terms mostly used to describe a metal that is able to be drawn into a wire.

Malleable is used to describe metals that are easily moulded through physical force.

so neither of these terms are appropriate.

I would say that u can’t really use rigid and flexible in the same sentence because they are contradictory and not likely to lead the reader to understand exactly what you mean. I would use either “adjustable” which emphasises its ability rather than property or “pliant” which whilst it indicates its ability to flex, its often used to describe metals ability to be adjusted (e.g. the property of a paperclip to bend could be described as pliant).