How Do I Use Properly Case. .When in Mysql

CASE case_value
    WHEN when_value THEN statements
    [WHEN when_value THEN statements]
    ELSE statements
END 

Or:

CASE
WHEN <search_condition> THEN statements
[WHEN <search_condition> THEN statements] 
ELSE statements
END 

here CASE is an expression in 2nd scenario search_condition will evaluate and if no search_condition is equal then execute else

SELECT
   CASE course_enrollment_settings.base_price
    WHEN course_enrollment_settings.base_price = 0      THEN 1

should be

SELECT
   CASE 
    WHEN course_enrollment_settings.base_price = 0      THEN 1

CASE course_enrollment_settings.base_price is wrong here, it should be just CASE

SELECT 
CASE 
WHEN course_enrollment_settings.base_price = 0      THEN 1 
WHEN course_enrollment_settings.base_price<101      THEN 2 
WHEN course_enrollment_settings.base_price>100 AND    
                  course_enrollment_settings.base_price<201 THEN 3 
    ELSE 6 
END AS 'calc_base_price', 
course_enrollment_settings.base_price 
FROM 
  course_enrollment_settings 
WHERE course_enrollment_settings.base_price = 0 

Some explanations. Your original query will be executed as :

SELECT 
CASE 0
WHEN 0=0 THEN 1 -- condition evaluates to 1, then 0 (from CASE 0)compares to 1 - false
WHEN 0<1 THEN 2 -- condition evaluates to 1,then 0 (from CASE 0)compares to 1 - false
WHEN 0>100 and 0<201 THEN 3 -- evaluates to 0 ,then 0 (from CASE 0)compares to 0 - true
ELSE 6, ...

it's why you always get 3

SELECT
   CASE 
    WHEN course_enrollment_settings.base_price = 0      THEN 1
    WHEN course_enrollment_settings.base_price>0 AND  
         course_enrollment_settings.base_price<=100     THEN 2
    WHEN course_enrollment_settings.base_price>100 AND   
         course_enrollment_settings.base_price<201      THEN 3
        ELSE 6
   END AS 'calc_base_price',
   course_enrollment_settings.base_price
FROM
    course_enrollment_settings
WHERE course_enrollment_settings.base_price = 0

There are two variants of CASE, and you're not using the one that you think you are.

What you're doing

CASE case_value
    WHEN when_value THEN statement_list
    [WHEN when_value THEN statement_list] ...
    [ELSE statement_list]
END CASE

Each condition is loosely equivalent to a if (case_value == when_value) (pseudo-code).

However, you've put an entire condition as when_value, leading to something like:

if (case_value == (case_value > 100))

Now, (case_value > 100) evaluates to FALSE, and is the only one of your conditions to do so. So, now you have:

if (case_value == FALSE)

FALSE converts to 0 and, through the resulting full expression if (case_value == 0) you can now see why the third condition fires.

What you're supposed to do

Drop the first course_enrollment_settings so that there's no case_value, causing MySQL to know that you intend to use the second variant of CASE:

CASE
    WHEN search_condition THEN statement_list
    [WHEN search_condition THEN statement_list] ...
    [ELSE statement_list]
END CASE

Now you can provide your full conditionals as search_condition.

Also, please read the documentation for features that you use.

I think part of it is that you're stating the value you're selecting after CASE, and then using WHEN x = y syntax afterward, which is a combination of two different methods of using CASE. It should either be

CASE X
  WHEN a THEN ...
  WHEN b THEN ...

or

CASE
  WHEN x = a THEN ...
  WHEN x = b THEN ...