How to get Scilab 6.0.1 working on Ubuntu 18.04 LTS?

* Repository-based method (Scilab itself and ATOMS will not work)

Update 2020-12-07. Nowadays Scilab is broken again as indicated in bug 1884277.

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* Binary download method (fully-functional, seems to be really recommended)

So if you need fully-functional Scilab you should remove deb-packaged version with

sudo apt-get purge scilab scilab scilab-cli scilab-data scilab-doc scilab-full-bin scilab-include scilab-minimal-bin scilab-sivp scilab-test
sudo apt-get autoremove

and use latest binary archive 6.1.0 from official site and run the commands below (download, extract, add to PATH, set shortcuts and MIME-association):

mkdir ~/Software
cd  ~/Software
wget https://www.scilab.org/download/6.1.0/scilab-6.1.0.bin.linux-x86_64.tar.gz
tar -xzf scilab-6.1.0.bin.linux-x86_64.tar.gz
cd scilab-6.1.0
echo "PATH=$PATH:/home/$USER/Software/scilab-6.1.0/bin" >> ~/.bashrc
echo "PATH=$PATH:/home/$USER/Software/scilab-6.1.0/bin" >> ~/.profile
mkdir -p ~/.local/share/applications
cp -a ~/Software/scilab-6.1.0/share/{icons,applications,mime} ~/.local/share/
update-mime-database ~/.local/share/mime/
update-menus

The ATOMS and other components will work as expected. Do not forget to install build-essential package to run Xcos Modelica simulations.

* AppImage download method (fully-functional)

We need to download the latest release from corresponding page or manually:

mkdir ~/Software
cd ~/Software
wget https://github.com/davidcl/Scilab.AppDir/releases/download/6.1.0-1/Scilab-x86_64.AppImage
chmod +x Scilab-x86_64.AppImage
ln -s Scilab-x86_64.AppImage scilab

and then add it to PATH with

echo "PATH=$PATH:/home/$USER/Software/" >> ~/.bashrc
echo "PATH=$PATH:/home/$USER/Software/" >> ~/.profile

As the result you will get Scilab working. But there is no MIME associations (yet).

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If you want to get Scilab 5.5.2 working on Ubuntu 18.04.1 LTS see other answer. But be careful with libcurl4 removal!