I don't think your problem is growing in containers, but growing without sun. You need to pick vegetables that do not require much sun. Al

Where I place the containers I do get pretty much full sun from about 10am to 5pm

I suspect that the problem is your choice of potting mix. Take a few moments to check out some of the very informative threads in this forum regarding the importance of finding or making a porous, fast draining potting medium.

In answer to your question, you can grow almost any vegetable in a container if the pot is large enough (at least 5-10 gallons) and the potting mix is fast draining, like the 5-1-1 discussed on this forum. I've successfully grown many different veggies in containers with 5-6 hours of sun, including watermelons and pumpkins in 25-gallon containers.

Japanese eggplants are great in containers, very productive, even with just 4 hours of direct sunlight a day, which is all I have for my containers.

I've also had great results using organic compost mixes.

Here is a link that might be useful: Photos of organic containers

I am surprised that your Cucumber did not do well in container. Beside the container you have to have something built to climb on it. Also make sure your containers and whatever soil you use has good drainage properties.

It would be also helpful to know what zone you are in?

There is a very useful book entitled, "The Bountiful Container" written by Rose Marie Nichols McGee and Maggie Stuckey that gives a lot of useful information about growing vegetables in containers. You might want to check it out. I found it to be very inspiring. If you have sun and heat and good drainage you should have success -- the rest is trial and error and good eats. enjoy!!