There are two installations for Python on Azure VM for Data Science, which include system level & Anaconda level.
As @darthbith said, it shows the path /usr/local/bin/pip when you run the command which pip, which is belong to system level.
You need to move to the path bin of Anaconda and install the modules you want using the ./pip command for the current Anaconda, as below using jupyter terminal.
# For example, using anaconda for Python 2
nbuser@nbserver:~$ cd anaconda2_20/bin
# Using the Anaconda pip to install modules
nbuser@nbserver:~/anaconda2_20/bin$ ./pip install azure-storage --upgrade
# Then see the content below
Collecting azure-storage
Downloading azure_storage-0.33.0-py2-none-any.whl (182kB)
100% |################################| 184kB 2.9MB/s
Collecting requests (from azure-storage)
Downloading requests-2.12.1-py2.py3-none-any.whl (574kB)
100% |################################| 583kB 1.7MB/s
Requirement already up-to-date: azure-nspkg in /home/nbcommon/anaconda2_20/lib/python2.7/site-packages (from azure-storage)
Requirement already up-to-date: azure-common in /home/nbcommon/anaconda2_20/lib/python2.7/site-packages (from azure-storage)
Requirement already up-to-date: futures in /home/nbcommon/anaconda2_20/lib/python2.7/site-packages (from azure-storage)
Collecting cryptography (from azure-storage)
Downloading cryptography-1.5.3.tar.gz (400kB)
.....
Then the azure-storgae module be upgraded for the current Anaconda.
Hope it helps.