Here's the implementation:

```python
def even_odd_count(num):
    """Given an integer. return a tuple that has the number of even and odd digits respectively.

     Example:
        even_odd_count(-12) ==> (1, 1)
        even_odd_count(123) ==> (1, 2)
    """
    num = abs(num)
    even_count = 0
    odd_count = 0
    for digit in str(num):
        if int(digit) % 2 == 0:
            even_count += 1
        else:
            odd_count += 1
    return (even_count, odd_count)
```


```python

def int_to_mini_roman(number):
    """
    Given a positive integer, obtain its roman numeral equivalent as a string,
    and return it in lowercase.
    Restrictions: 1 <= num <= 1000

    Examples:
    >>> int_to_mini_roman(19) == 'xix'
    >>> int_to_mini_roman(152) == 'clii'
    >>> int_to_mini_roman(426) == 'cdxxvi'
    """
    # Mapping of values to roman numeral symbols (uppercase for clarity, then lowercased)
    val_to_roman = [
        (1000, 'M'),
        (900, 'CM'),
        (500, 'D'),
        (400, 'CD'),
        (100, 'C'),
        (90, 'XC'),
        (50, 'L'),
        (40, 'XL'),
        (10, 'X'),
        (9, 'IX'),
        (5, 'V'),
        (4, 'IV'),
        (1, 'I')
    ]

    result = ''
    num = number
    for value, symbol in val_to_roman:
        while num >= value:
            result += symbol
            num -= value
    return result.lower()

```


```python

def right_angle_triangle(a, b, c):
    '''
    Given the lengths of the three sides of a triangle. Return True if the three
    sides form a right-angled triangle, False otherwise.
    A right-angled triangle is a triangle in which one angle is right angle or
    90 degree.
    Example:
    right_angle_triangle(3, 4, 5) == True
    right_angle_triangle(1, 2, 3) == False
    '''
    sides = sorted([a, b, c])
    # Check triangle inequality and Pythagorean theorem
    return sides[0] > 0 and sides[0]**2 + sides[1]**2 == sides[2]**2

```


```python

def find_max(words):
    """
    Returns the word with the maximum number of unique characters.
    If multiple words have the same maximum, returns the lexicographically smallest.
    """
    best_word = None
    best_unique_count = -1

    for word in words:
        unique_count = len(set(word))
        if unique_count > best_unique_count:
            best_unique_count = unique_count
            best_word = word
        elif unique_count == best_unique_count and word < best_word:
            best_word = word

    return best_word

```


```python

def eat(number, need, remaining):
    """
    You're a hungry rabbit, and you already have eaten a certain number of carrots,
    but now you need to eat more carrots to complete the day's meals.
    you should return an array of [ total number of eaten carrots after your meals,
                                    the number of carrots left after your meals ]
    if there are not enough remaining carrots, you will eat all remaining carrots, but will still be hungry.

    Example:
    * eat(5, 6, 10) -> [11, 4]
    * eat(4, 8, 9) -> [12, 1]
    * eat(1, 10, 10) -> [11, 0]
    * eat(2, 11, 5) -> [7, 0]

    Variables:
    @number : integer
        the number of carrots that you have eaten.
    @need : integer
        the number of carrots that you need to eat.
    @remaining : integer
        the number of remaining carrots thet exist in stock

    Constrain:
    * 0 <= number <= 1000
    * 0 <= need <= 1000
    * 0 <= remaining <= 1000

    Have fun :)
    """
    eaten = min(need, remaining)
    total_eaten = number + eaten
    remaining_after = remaining - eaten
    return [total_eaten, remaining_after]

```


Here's the implementation for the function you described:

```python
def do_algebra(operator, operand):
    """
    Given two lists operator, and operand. The first list has basic algebra operations, and
    the second list is a list of integers. Use the two given lists to build the algebric
    expression and return the evaluation of this expression.

    The basic algebra operations:
    Addition ( + )
    Subtraction ( - )
    Multiplication ( * )
    Floor division ( // )
    Exponentiation ( ** )

    Example:
    operator['+', '*', '-']
    array = [2, 3, 4, 5]
    result = 2 + 3 * 4 - 5
    => result = 9

    Note:
        The length of operator list is equal to the length of operand list minus one.
        Operand is a list of of non-negative integers.
        Operator list has at least one operator, and operand list has at least two operands.

    """
    # Start with the first operand
    result = operand[0]

    # Apply each operator to the running result and the next operand
    for i, op in enumerate(operator):
        next_val = operand[i + 1]
        if op == '+':
            result = result + next_val
        elif op == '-':
            result = result - next_val
        elif op == '*':
            result = result * next_val
        elif op == '//':
            result = result // next_val
        elif op == '**':
            result = result ** next_val

    return result
```


```python

def solve(s):
    result = []
    has_letter = False
    for ch in s:
        if ch.isalpha():
            has_letter = True
            if ch.islower():
                result.append(ch.upper())
            else:
                result.append(ch.lower())
        else:
            result.append(ch)
    if not has_letter:
        return ''.join(reversed(result))
    return ''.join(result)

```


```python
import hashlib

def string_to_md5(text):
    """
    Given a string 'text', return its md5 hash equivalent string.
    If 'text' is an empty string, return None.

    >>> string_to_md5('Hello world') == '3e25960a79dbc69b674cd4ec67a72c62'
    """
    if text == "":
        return None
    return hashlib.md5(text.encode()).hexdigest()
```


Traceback (most recent call last):
  File "<string>", line 34, in <module>
    check(generate_integers)
    ~~~~~^^^^^^^^^^^^^^^^^^^
  File "<string>", line 25, in check
    assert candidate(2, 10) == [2, 4, 6, 8], "Test 1"
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
AssertionError: Test 1

```python
def generate_integers(a, b):
    """
    Given two positive integers a and b, return the even digits between a
    and b, in ascending order.

    For example:
    generate_integers(2, 8) => [2, 4, 6, 8]
    generate_integers(8, 2) => [2, 4, 6, 8]
    generate_integers(10, 14) => []
    """
    low = min(a, b)
    high = max(a, b)
    result = []
    for num in range(low, high + 1):
        if num % 2 == 0:
            result.append(num)
    return result
```